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Simplifying 5x2 + -7x + -40 = x2 + 5x Reorder the terms: -40 + -7x + 5x2 = x2 + 5x Reorder the terms: -40 + -7x + 5x2 = 5x + x2 Solving -40 + -7x + 5x2 = 5x + x2 Solving for variable 'x'. Reorder the terms: -40 + -7x + -5x + 5x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: -7x + -5x = -12x -40 + -12x + 5x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -40 + -12x + 4x2 = 5x + x2 + -5x + -1x2 Reorder the terms: -40 + -12x + 4x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -40 + -12x + 4x2 = 0 + x2 + -1x2 -40 + -12x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -40 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -3x + x2) = 0 Factor a trinomial. 4((-2 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2, 5}
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