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Simplifying x + 14 = (x + -6)(x + -6) Reorder the terms: 14 + x = (x + -6)(x + -6) Reorder the terms: 14 + x = (-6 + x)(x + -6) Reorder the terms: 14 + x = (-6 + x)(-6 + x) Multiply (-6 + x) * (-6 + x) 14 + x = (-6(-6 + x) + x(-6 + x)) 14 + x = ((-6 * -6 + x * -6) + x(-6 + x)) 14 + x = ((36 + -6x) + x(-6 + x)) 14 + x = (36 + -6x + (-6 * x + x * x)) 14 + x = (36 + -6x + (-6x + x2)) Combine like terms: -6x + -6x = -12x 14 + x = (36 + -12x + x2) Solving 14 + x = 36 + -12x + x2 Solving for variable 'x'. Reorder the terms: 14 + -36 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Combine like terms: 14 + -36 = -22 -22 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Combine like terms: x + 12x = 13x -22 + 13x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Reorder the terms: -22 + 13x + -1x2 = 36 + -36 + -12x + 12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -22 + 13x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -22 + 13x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -22 + 13x + -1x2 = 0 + x2 + -1x2 -22 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -22 + 13x + -1x2 = 0 Factor a trinomial. (-11 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Subproblem 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 = {11, 2}
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