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Simplifying x(x + 1) = 4 + -1(x + 2)(x + 2) Reorder the terms: x(1 + x) = 4 + -1(x + 2)(x + 2) (1 * x + x * x) = 4 + -1(x + 2)(x + 2) (1x + x2) = 4 + -1(x + 2)(x + 2) Reorder the terms: 1x + x2 = 4 + -1(2 + x)(x + 2) Reorder the terms: 1x + x2 = 4 + -1(2 + x)(2 + x) Multiply (2 + x) * (2 + x) 1x + x2 = 4 + -1(2(2 + x) + x(2 + x)) 1x + x2 = 4 + -1((2 * 2 + x * 2) + x(2 + x)) 1x + x2 = 4 + -1((4 + 2x) + x(2 + x)) 1x + x2 = 4 + -1(4 + 2x + (2 * x + x * x)) 1x + x2 = 4 + -1(4 + 2x + (2x + x2)) Combine like terms: 2x + 2x = 4x 1x + x2 = 4 + -1(4 + 4x + x2) 1x + x2 = 4 + (4 * -1 + 4x * -1 + x2 * -1) 1x + x2 = 4 + (-4 + -4x + -1x2) Combine like terms: 4 + -4 = 0 1x + x2 = 0 + -4x + -1x2 1x + x2 = -4x + -1x2 Solving 1x + x2 = -4x + -1x2 Solving for variable 'x'. Reorder the terms: 1x + 4x + x2 + x2 = -4x + -1x2 + 4x + x2 Combine like terms: 1x + 4x = 5x 5x + x2 + x2 = -4x + -1x2 + 4x + x2 Combine like terms: x2 + x2 = 2x2 5x + 2x2 = -4x + -1x2 + 4x + x2 Reorder the terms: 5x + 2x2 = -4x + 4x + -1x2 + x2 Combine like terms: -4x + 4x = 0 5x + 2x2 = 0 + -1x2 + x2 5x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {0, -2.5}
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