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Simplifying x(x + 1) = x + (x + 1) + 41 Reorder the terms: x(1 + x) = x + (x + 1) + 41 (1 * x + x * x) = x + (x + 1) + 41 (1x + x2) = x + (x + 1) + 41 Reorder the terms: 1x + x2 = x + (1 + x) + 41 Remove parenthesis around (1 + x) 1x + x2 = x + 1 + x + 41 Reorder the terms: 1x + x2 = 1 + 41 + x + x Combine like terms: 1 + 41 = 42 1x + x2 = 42 + x + x Combine like terms: x + x = 2x 1x + x2 = 42 + 2x Solving 1x + x2 = 42 + 2x Solving for variable 'x'. Reorder the terms: -42 + 1x + -2x + x2 = 42 + 2x + -42 + -2x Combine like terms: 1x + -2x = -1x -42 + -1x + x2 = 42 + 2x + -42 + -2x Reorder the terms: -42 + -1x + x2 = 42 + -42 + 2x + -2x Combine like terms: 42 + -42 = 0 -42 + -1x + x2 = 0 + 2x + -2x -42 + -1x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -42 + -1x + x2 = 0 Factor a trinomial. (-6 + -1x)(7 + -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 '(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 = 7Solution
x = {-6, 7}
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