x2 + 6x + 20 = 35
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 9 = 24 + 9
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 9 = 24 + 9
(x + 3)2 = 33
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 9 = 24 + 9
(x + 3)2 = 33
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 9 = 24 + 9
(x + 3)2 = 33
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
x2 + 6x = 15
x2 + 6x + 9 = 24 + 9
(x + 3)2 = 33
x2 + 6x + 20 = 35
x2 + 6x – 15 = 0
2
6
x2 + 6x = 15 (
2)
x2 + 6x + 9 = 24 + 9
(x + 3)2 = 33
x2 + 12x – 4 = 18
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x + 36 = 22 +36
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x + 36 = 22 +36
(x + 6)2 = 58
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x + 36 = 22 +36
(x + 6)2 = 58
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x + 36 = 22 +36
(x + 6)2 = 58
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0
x2 + 12x = 22
x2 + 12x + 36 = 22 +36
(x + 6)2 = 58
x2 + 12x – 4 = 18
x2 + 12x – 22 = 0 2
12
x2 + 12x = 22 (
2)
x2 + 12x + 36 = 22 +36
(x + 6)2 = 58
3x2 + 12x – 4 = 18
3x2 + 12x – 4 = 18
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3
3
3
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3
32
x + 4x = 3
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3
32
x + 4x = 3
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3 4 2
32
(
2 )
x + 4x = 3
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3 4 2
32
(
2 )
x + 4x = 3
x + 4x + 4
2
22
= 3+
4
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3 4 2
32
(
2 )
x + 4x = 3
x
2
22
+ 4x + 4 = 3 +
34
2
(x + 2) = 3
4
3x2 + 12x – 4 = 18
3x2 + 12x = 22
3 22 3 4 2
32
(
2 )
x + 4x = 3
x
2
22
+ 4x + 4 = 3 +
34
2
(x + 2) = 3
4
ax2 + bx + c = 0
ax2 + bx + c = 0
1. Add -c to both sides.
ax2 + bx + c = 0
1. Add -c to both sides.
2. Divide both sides by a.
ax2 + bx + c = 0
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
ax2 + bx + c = 0
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
ax2 + bx + c = 0
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
5. Take the square roots of both sides.
ax2 + bx + c = 0
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
5. Take the square roots of both sides.
6. Perform transformations as
necessary to solve for x.
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
5x + 9x – 8 = 0
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
5x + 9x – 8 = 0
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
5x + 9x – 8 = 0
5x2 + 9x = 8
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
2
ax2 + bx + c = 0
ax2 + bx + c = 0
ax2 + bx = -c
ax2 + bx + c = 0
ax2 + bx = -c
a
a
a
ax2 + bx + c = 0
ax2 + bx = -c
a
a
a
-c
b
2
x +a x = a
ax2 + bx + c = 0
ax2 + bx = -c
a
a
a
-c
b
2
x +a x = a
b
a÷2
ax2 + bx + c = 0
ax2 + bx = -c
a
a
a
-c
b
2
x +a x = a
b
a÷2
b 1
a• 2
ax2 + bx + c = 0
ax2 + bx = -c
a
a
a
-c
b
2
x +a x = a
b
a÷2
b 1
a• 2
b
2a
b
a÷2
b 1
a• 2
b
2a
b
a÷2
b 1
a• 2
b
2a
9
5÷2
b
a÷2
b 1
a• 2
b
2a
9
5÷2
9 1
5 • 2
b
a÷2
b 1
a• 2
b
2a
9
5÷2
9 1
5 • 2
9
10
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
2
9
(
5
÷2)
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
9 2
(
10
)
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
9 2
(
10
)
8 81
81
9
2
x + 5 x+ 100 = 5 +100
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
Factor
the
left
side.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
9 2
(
10
)
8 81
81
9
2
x + 5 x+ 100 = 5 +100
2
Start
with
equation
in
form:
ax2
+
bx
+
c
=
0
Add
-c
to
both
sides.
Divide
both
sides
by
a.
The
new
coefficient
of
x
is
b/a
Add
(b/2a)2
to
both
sides.
Factor
the
left
side.
5x + 9x – 8 = 0
5x2 + 9x = 8
5 5
5
8
9
2
x +5 x = 5
9 2
(
10
)
8 81
81
9
2
x + 5 x+ 100 = 5 +100
2
(x
241
9 2
+10) = 100
Factor
the
left
side.
(x
241
9 2
+10) = 100
Factor
the
left
side.
Take
the
square
roots
of
both
sides.
(x
241
9 2
+10) = 100
Factor
the
left
side.
Take
the
square
roots
of
both
sides.
(x
241
9 2
+10) = 100
Factor
the
left
side.
Take
the
square
roots
of
both
sides.
Perform
transformations
as
necessary
to
solve
for
x.
(x
241
9 2
+10) = 100
Factor
the
left
side.
Take
the
square
roots
of
both
sides.
Perform
transformations
as
necessary
to
solve
for
x.
(x
241
9 2
+10) = 100
Factor
the
left
side.
Take
the
square
roots
of
both
sides.
Perform
transformations
as
necessary
to
solve
for
x.
(x
241
9 2
+10) = 100
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
2. Divide both sides by a.
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
5. Take the square roots of both sides.
To solve a quadratic equation in the
form, ax2 + bx + c = 0, by completing
the square, do the following:
1. Add -c to both sides.
2. Divide both sides by a.
3. Add (b/2a)2 to both sides.
4. Factor the left side.
5. Take the square roots of both sides.
6. Perform transformations as
necessary to solve for x.