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Simplifying 84 = (x + 5) * x Reorder the terms: 84 = (5 + x) * x Reorder the terms for easier multiplication: 84 = x(5 + x) 84 = (5 * x + x * x) 84 = (5x + x2) Solving 84 = 5x + x2 Solving for variable 'x'. Reorder the terms: 84 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 84 + -5x + -1x2 = 0 + x2 + -1x2 84 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 84 + -5x + -1x2 = 0 Factor a trinomial. (7 + -1x)(12 + x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {7, -12}
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