Why should we learn this?
The Square Root Property
One application is to use square roots in city
planning.
Objective: To solve quadratic
equations using square roots.
Review
What is the “Golden Rule” of solving
equations?
Answer: What you do to one side of an
equation, you must do to the ________ side.
What does quadratic mean?
Answer: variable is ________ (to 2nd power)
What is the opposite of squaring a
number?
Answer: Taking the square ________
What if…
we can’t factor the equation?
When there’s no “B” term, we can
easily use the Square Root
Property to solve quadratic
equations.
Ax2
REFLECT
+ Bx + C = 0
Question: How have we solved
quadratic equations before?
Answer: By ____________ and using
the Zero Factor Property.
Example: 2x2 - 7x = 15
2x2 – 7x – 15 = 0
(2x + 3)(x – 5) = 0
2x + 3 = 0 or x – 5 = 0
X = {-3/2, 5}
Square Root Property
If x and k are complex numbers,
and x 2 = k , then
x = k or x = − k .
(or x = ± k ).
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Steps for Solving Quadratic
Equations with no “B” term.
1. Isolate the ________ term.
2. Apply the Square Root Property.
(Take the square root of both
sides.)
3. Solve.
4. Check solutions.
Examples
A) Solve t2 – 25 = 0.
Any time you are solving a
quadratic equation, you must
give ____ possible solutions.
(In other words, be sure to use
the ± symbol .)
Try these.
Think, pair, share…
b) Solve 3n2 + 12 = 12.
More Examples
e) (t + 8)2 = 9
Special Note
C) Solve x2 = 54
D) 3x2 – 75 = 0
More Examples
f ) (5k − 2)2 = 12
g ) (4m − 7) 2 = −27
h) 2 g 2 + 32 = 0
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