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Simplifying x(x + 1) = 992 Reorder the terms: x(1 + x) = 992 (1 * x + x * x) = 992 (1x + x2) = 992 Solving 1x + x2 = 992 Solving for variable 'x'. Reorder the terms: -992 + 1x + x2 = 992 + -992 Combine like terms: 992 + -992 = 0 -992 + 1x + x2 = 0 Factor a trinomial. (-32 + -1x)(31 + -1x) = 0Subproblem 1
Set the factor '(-32 + -1x)' equal to zero and attempt to solve: Simplifying -32 + -1x = 0 Solving -32 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -1x = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1x = 0 + 32 -1x = 0 + 32 Combine like terms: 0 + 32 = 32 -1x = 32 Divide each side by '-1'. x = -32 Simplifying x = -32Subproblem 2
Set the factor '(31 + -1x)' equal to zero and attempt to solve: Simplifying 31 + -1x = 0 Solving 31 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -1x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -1x = 0 + -31 -1x = 0 + -31 Combine like terms: 0 + -31 = -31 -1x = -31 Divide each side by '-1'. x = 31 Simplifying x = 31Solution
x = {-32, 31}
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