1. 1.5 Square Root and Completing the Square

2. 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

3. Solve by Taking Square Roots
X = ± 2i

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

5. Solve by Taking Square Roots
X = ± 3

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

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

8. Solve by Taking Square Roots
x2 = 243
X = ± 3i 3

9. MENTAL BREAK!!

10. Completing the Square

11. 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.

12. 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

13. 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.

14. Example 1:

15. Example 2:

16. Example 3:

17. Example 4:

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