Completing the Square, Quadratic Formula

Factoring and using square roots work well, but only in special cases Not factorable? A2 ≠ C? Then what?

Completing the Square If a quadratic is not factorable, we can use a method to “fix” the quadratic Makes the quadratic factorable End Goal: Use the square root method learned previously (ax + b)2 = c

Completing the Square Ex. x2 – 2x – 6 = 0 Notice, cannot factor using GCF or other method Steps: 1) Write in ax2 +bx = -c Move constant term

Step 2: Find the coefficient of x; divide by 2, square the result, then add to both sides: x2 -2x +1 = 6 + 1 X2 – 2x + 1 = 7 (Perfect Square Trinomial)

Step 3: Factor the perfect square trinomial on the left side: (x – 1)2 = 7 Step 4: Solve using square roots:

Example. Solve by using completing the square: A) x2 – 4x = 16 B) 2x2 + 7x – 15 = 0

Quadratic Formula Many times, we will have decimal roots or imaginary roots we cannot find by factoring or graphing All roots may be found using the quadratic formula (complex or real):

Example. Find the solutions to 8x2 – 4x -1 = 0 using the quadratic formula.

Example. Find the roots of x2 + 2x + 13 = 0 using the quadratic formula.

Assignment Pg. 93 #25-45 odd