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Simplifying 7x2 + -6x + -11 = -1x2 + -2x + 13 Reorder the terms: -11 + -6x + 7x2 = -1x2 + -2x + 13 Reorder the terms: -11 + -6x + 7x2 = 13 + -2x + -1x2 Solving -11 + -6x + 7x2 = 13 + -2x + -1x2 Solving for variable 'x'. Reorder the terms: -11 + -13 + -6x + 2x + 7x2 + x2 = 13 + -2x + -1x2 + -13 + 2x + x2 Combine like terms: -11 + -13 = -24 -24 + -6x + 2x + 7x2 + x2 = 13 + -2x + -1x2 + -13 + 2x + x2 Combine like terms: -6x + 2x = -4x -24 + -4x + 7x2 + x2 = 13 + -2x + -1x2 + -13 + 2x + x2 Combine like terms: 7x2 + x2 = 8x2 -24 + -4x + 8x2 = 13 + -2x + -1x2 + -13 + 2x + x2 Reorder the terms: -24 + -4x + 8x2 = 13 + -13 + -2x + 2x + -1x2 + x2 Combine like terms: 13 + -13 = 0 -24 + -4x + 8x2 = 0 + -2x + 2x + -1x2 + x2 -24 + -4x + 8x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 -24 + -4x + 8x2 = 0 + -1x2 + x2 -24 + -4x + 8x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -24 + -4x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -1x + 2x2) = 0 Factor a trinomial. 4((-3 + -2x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
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 = 2Solution
x = {-1.5, 2}
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