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Simplifying x(x + 2) = 4 + 2x(x + 3) Reorder the terms: x(2 + x) = 4 + 2x(x + 3) (2 * x + x * x) = 4 + 2x(x + 3) (2x + x2) = 4 + 2x(x + 3) Reorder the terms: 2x + x2 = 4 + 2x(3 + x) 2x + x2 = 4 + (3 * 2x + x * 2x) 2x + x2 = 4 + (6x + 2x2) Solving 2x + x2 = 4 + 6x + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 2x + -6x + x2 + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2 Combine like terms: 2x + -6x = -4x -4 + -4x + x2 + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -4 + -4x + -1x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2 Reorder the terms: -4 + -4x + -1x2 = 4 + -4 + 6x + -6x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 -4 + -4x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2 -4 + -4x + -1x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -4 + -4x + -1x2 = 0 + 2x2 + -2x2 -4 + -4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 4x + x2) = 0 Factor a trinomial. -1((2 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2, -2}
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