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Simplifying 4(5x + 20) + 4(x + 4) = -2(x + 4)(5x + 20) Reorder the terms: 4(20 + 5x) + 4(x + 4) = -2(x + 4)(5x + 20) (20 * 4 + 5x * 4) + 4(x + 4) = -2(x + 4)(5x + 20) (80 + 20x) + 4(x + 4) = -2(x + 4)(5x + 20) Reorder the terms: 80 + 20x + 4(4 + x) = -2(x + 4)(5x + 20) 80 + 20x + (4 * 4 + x * 4) = -2(x + 4)(5x + 20) 80 + 20x + (16 + 4x) = -2(x + 4)(5x + 20) Reorder the terms: 80 + 16 + 20x + 4x = -2(x + 4)(5x + 20) Combine like terms: 80 + 16 = 96 96 + 20x + 4x = -2(x + 4)(5x + 20) Combine like terms: 20x + 4x = 24x 96 + 24x = -2(x + 4)(5x + 20) Reorder the terms: 96 + 24x = -2(4 + x)(5x + 20) Reorder the terms: 96 + 24x = -2(4 + x)(20 + 5x) Multiply (4 + x) * (20 + 5x) 96 + 24x = -2(4(20 + 5x) + x(20 + 5x)) 96 + 24x = -2((20 * 4 + 5x * 4) + x(20 + 5x)) 96 + 24x = -2((80 + 20x) + x(20 + 5x)) 96 + 24x = -2(80 + 20x + (20 * x + 5x * x)) 96 + 24x = -2(80 + 20x + (20x + 5x2)) Combine like terms: 20x + 20x = 40x 96 + 24x = -2(80 + 40x + 5x2) 96 + 24x = (80 * -2 + 40x * -2 + 5x2 * -2) 96 + 24x = (-160 + -80x + -10x2) Solving 96 + 24x = -160 + -80x + -10x2 Solving for variable 'x'. Reorder the terms: 96 + 160 + 24x + 80x + 10x2 = -160 + -80x + -10x2 + 160 + 80x + 10x2 Combine like terms: 96 + 160 = 256 256 + 24x + 80x + 10x2 = -160 + -80x + -10x2 + 160 + 80x + 10x2 Combine like terms: 24x + 80x = 104x 256 + 104x + 10x2 = -160 + -80x + -10x2 + 160 + 80x + 10x2 Reorder the terms: 256 + 104x + 10x2 = -160 + 160 + -80x + 80x + -10x2 + 10x2 Combine like terms: -160 + 160 = 0 256 + 104x + 10x2 = 0 + -80x + 80x + -10x2 + 10x2 256 + 104x + 10x2 = -80x + 80x + -10x2 + 10x2 Combine like terms: -80x + 80x = 0 256 + 104x + 10x2 = 0 + -10x2 + 10x2 256 + 104x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 256 + 104x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(128 + 52x + 5x2) = 0 Factor a trinomial. 2((32 + 5x)(4 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 5x)' equal to zero and attempt to solve: Simplifying 32 + 5x = 0 Solving 32 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + 5x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 5x = 0 + -32 5x = 0 + -32 Combine like terms: 0 + -32 = -32 5x = -32 Divide each side by '5'. x = -6.4 Simplifying x = -6.4Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-6.4, -4}
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