1.5 Square Root and Completing the Square

Solving with Square Roots Get x2 or the binomial squared by itself Take the square root of BOTH sides of the equal sign Don’t forget the  sign Simplify

Solve by Taking Square Roots X = ± 2i

Solve by Taking Square Roots X = ± 3 2

Solve by Taking Square Roots X = ± 3

Solve by Taking Square Roots X = -4 ± 3 2

Solve by Taking Square Roots 5. 5(x – 4)2 = 125 X = -1 and 9

Solve by Taking Square Roots 6. - 9x2 = 243 X = ± 3i 3

MENTAL BREAK!!

Completing the Square

Completing the Square Completing the square is used for all those problems that don’t factor!! It is used to solve these equations for the variable. It gets a little messy when a is not 1.

Completing the Square ax2 + bx + c = 0 Is another way to solve a quadratic equation. ax2 + bx + c = 0 a needs to be 1. b is easier when even. c needs to be moved to the other side of the = sign

Steps to Completing the Square 1. Move the constant to the other side. 2. Add to BOTH sides of the eqn. 3. Factor! 4. Take the square root of both sides. 5. Solve for x.

Example 1:

Example 2:

Example 3:

Example 4:

HOMEWORK: Page 267 #51-67 ODD Skip #59 Page 286 #32-35, 47-51 SKIP #50