Aim #53: How do we solve quadratic equations by completing the square?
Homework: Handout
Do Now: Solve the equation for b by factoring:
2
2
2b - 9b = 3b - 4b - 14
Example 1: Solve for x:
2
x + 6x = 12
Can you factor the above equation? ______. Bycompleting the square, we can solve
the quadratic equation another way.
2
x + 6x = 12
(gather all terms on one side of equation)
1
2
2
(complete the square: [ (6)]
(factor the perfect square)
(add the constant to the other side of the equation)
(take the square root of both sides)
=±
(solve for x)
x=
or x =
Example 2: Solve for x:
2
4x - 40x + 94 = 0
*Leave all radicals in simplest form. To be in simplest form, the denominator of a
fraction should not be irrational. You must make sure to "rationalize the denominator".
Solve each equation by completing the square. Simplify all radicals when necessary.
2
1)
x - 2x = 12
3)
2y + 8y = 7
2
2)
4)
2
n - 6n = 2
2
2x + 3x - 5 = 4
5) a. Solve the following quadratic equation by factoring:
2
x -x =3
b. Solve the following quadratic equation by completing the square:
2
x -x =3
2
6) 2x + 4x + 1 = 0
2
8) -x + 8x = -6
2
10) -2x - 7x - 5 = 0
2
7) -2x + 4x + 8 = 0
2
9) x + 4x = -1
2
11) 4x - 12x + 7 = 0
LET'S SUM IT UP!!!
When a quadratic equation is not factorable, another method we can use to
solve it is called completing the square.
Completing the square can be used to find solutions that are irrational or rational.