3. Write an equation in which the quadratic expression 2x^2-2x-12 equals 0. Show the expression in factored form and explain what your solutions mean for the equation. Show your work.

Step-by-step explanation:

2x²-2x-12 = 2 (x²-x - 6)

but : x²-x - 6 = x² - 2 (1/2) x + (1/2) ² - (1/2) ² - 6

= (x - 1/2) ² - 1/4 - 6

= (x - 1/2) ² - 25/4

x²-x - 6 = (x - 1/2) ² - (5/2) ²

by identity; a² - b² = (a - b) (a + b)

x²-x - 6 = (x - 1/2 - 5/2) (x - 1/2 + 5/2)

x²-x - 6 = (x - 3) (x + 2)

so : 2x²-2x-12 = 2 (x - 3) (x + 2) = (2x-6) (x+2) ... (factored form)

now : 2x²-2x-12 = 0 : 2x - 6 = 0 or x+2 = 0

x = 3 or x = - 2 two solutions