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Simplifying x(x + 1) = 15 + -1x(2 + -1x) Reorder the terms: x(1 + x) = 15 + -1x(2 + -1x) (1 * x + x * x) = 15 + -1x(2 + -1x) (1x + x2) = 15 + -1x(2 + -1x) 1x + x2 = 15 + (2 * -1x + -1x * -1x) 1x + x2 = 15 + (-2x + 1x2) Solving 1x + x2 = 15 + -2x + 1x2 Solving for variable 'x'. Reorder the terms: -15 + 1x + 2x + x2 + -1x2 = 15 + -2x + 1x2 + -15 + 2x + -1x2 Combine like terms: 1x + 2x = 3x -15 + 3x + x2 + -1x2 = 15 + -2x + 1x2 + -15 + 2x + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + 3x + 0 = 15 + -2x + 1x2 + -15 + 2x + -1x2 -15 + 3x = 15 + -2x + 1x2 + -15 + 2x + -1x2 Reorder the terms: -15 + 3x = 15 + -15 + -2x + 2x + 1x2 + -1x2 Combine like terms: 15 + -15 = 0 -15 + 3x = 0 + -2x + 2x + 1x2 + -1x2 -15 + 3x = -2x + 2x + 1x2 + -1x2 Combine like terms: -2x + 2x = 0 -15 + 3x = 0 + 1x2 + -1x2 -15 + 3x = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -15 + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Solution
x = {5}
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