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

x/3-10=8

x/3=18

x=48

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15