Solve for all values of x by factoring. x^2 +x−27= 5x+5

Answer 1

To solve this equation by factoring, we need to first rewrite the equation in standard form by moving all terms to one side of the equation:

x^2 + x - 27 = 5x + 5
x^2 + x - 5x - 27 - 5 = 0
x^2 - 4x - 32 = 0

Now, we will factor the quadratic expression:

(x - 8)(x + 4) = 0

Setting each factor to zero gives us the possible values of x:

x - 8 = 0 or x + 4 = 0

x = 8 x = -4

Therefore, the values of x that satisfy the equation are x = 8 or x = -4.