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Simplifying x(x + 1) + 3 = 33 Reorder the terms: x(1 + x) + 3 = 33 (1 * x + x * x) + 3 = 33 (1x + x2) + 3 = 33 Reorder the terms: 3 + 1x + x2 = 33 Solving 3 + 1x + x2 = 33 Solving for variable 'x'. Reorder the terms: 3 + -33 + 1x + x2 = 33 + -33 Combine like terms: 3 + -33 = -30 -30 + 1x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -30 + 1x + x2 = 0 Factor a trinomial. (-6 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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 = {-6, 5}
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