Question

Solve the equation by factoring. 2x2 = 28 - x

x = -3.5 or x = 4
x = 2 or x = -7
x = -2 or x = 7
x= -4 or x = 3.5

Answer 1

2x^2 = 28 - x

-28+x -28+x

2x^2 + x - 28 = 0

ac=-56

m+p=-7,8

(2x-7)(2x+8)=0

2x-7+7=0+7

2x/2=7/2

x=3.5

2x+8-8=0-8

2x/2=-8/2

x= -4

Explanation:

1. subtract from right to left to get the equation in a standard form = 0
2. since there's no GCF and no two numbers that multiply to -28 and add to x, we can multiply a and c (-56), then find two numbers that multiply to ac and add to bx (-7,8).
3. factor the equation into two binomials and set them equal to zero. the binomials must start with the square root of the first term and end with the square root of the second term.
4. solve for x if the two binomials.

x=-4 or 3.5