Solving a Quadratic (x²) Equation

Three methods are ZPP, Square Roots, & Intersections. We are only able to use square roots when we can isolate x². The intersection method often is not practical withoug a graphing calculator.

ZPP Square Roots

2x² + 7x = 4 2x² – 6 = 0

2x² + 7x - 4 = 0 (set one side to 0) x² = 3 (isolate x² - not practical in other examples)

(2x -1)(x + 4) = 0 (factor) x = 1.73 or x = -1.73 (take square root)

2x – 1 = 0 or x + 4 = 0 (one factor must be 0)

x = ½ or x = -4

Intersections

2x² – x = 3

(graph each side of equation):

x = -1 or x = 1.5