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Simplifying 4(2 + -1x)(x + 2) + 20 = 36(x + 1) + -1x(2x + 7) Reorder the terms: 4(2 + -1x)(2 + x) + 20 = 36(x + 1) + -1x(2x + 7) Multiply (2 + -1x) * (2 + x) 4(2(2 + x) + -1x * (2 + x)) + 20 = 36(x + 1) + -1x(2x + 7) 4((2 * 2 + x * 2) + -1x * (2 + x)) + 20 = 36(x + 1) + -1x(2x + 7) 4((4 + 2x) + -1x * (2 + x)) + 20 = 36(x + 1) + -1x(2x + 7) 4(4 + 2x + (2 * -1x + x * -1x)) + 20 = 36(x + 1) + -1x(2x + 7) 4(4 + 2x + (-2x + -1x2)) + 20 = 36(x + 1) + -1x(2x + 7) Combine like terms: 2x + -2x = 0 4(4 + 0 + -1x2) + 20 = 36(x + 1) + -1x(2x + 7) 4(4 + -1x2) + 20 = 36(x + 1) + -1x(2x + 7) (4 * 4 + -1x2 * 4) + 20 = 36(x + 1) + -1x(2x + 7) (16 + -4x2) + 20 = 36(x + 1) + -1x(2x + 7) Reorder the terms: 16 + 20 + -4x2 = 36(x + 1) + -1x(2x + 7) Combine like terms: 16 + 20 = 36 36 + -4x2 = 36(x + 1) + -1x(2x + 7) Reorder the terms: 36 + -4x2 = 36(1 + x) + -1x(2x + 7) 36 + -4x2 = (1 * 36 + x * 36) + -1x(2x + 7) 36 + -4x2 = (36 + 36x) + -1x(2x + 7) Reorder the terms: 36 + -4x2 = 36 + 36x + -1x(7 + 2x) 36 + -4x2 = 36 + 36x + (7 * -1x + 2x * -1x) 36 + -4x2 = 36 + 36x + (-7x + -2x2) Combine like terms: 36x + -7x = 29x 36 + -4x2 = 36 + 29x + -2x2 Add '-36' to each side of the equation. 36 + -36 + -4x2 = 36 + 29x + -36 + -2x2 Combine like terms: 36 + -36 = 0 0 + -4x2 = 36 + 29x + -36 + -2x2 -4x2 = 36 + 29x + -36 + -2x2 Reorder the terms: -4x2 = 36 + -36 + 29x + -2x2 Combine like terms: 36 + -36 = 0 -4x2 = 0 + 29x + -2x2 -4x2 = 29x + -2x2 Solving -4x2 = 29x + -2x2 Solving for variable 'x'. Reorder the terms: -29x + -4x2 + 2x2 = 29x + -2x2 + -29x + 2x2 Combine like terms: -4x2 + 2x2 = -2x2 -29x + -2x2 = 29x + -2x2 + -29x + 2x2 Reorder the terms: -29x + -2x2 = 29x + -29x + -2x2 + 2x2 Combine like terms: 29x + -29x = 0 -29x + -2x2 = 0 + -2x2 + 2x2 -29x + -2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -29x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(29 + 2x) = 0 Ignore the factor -1.Subproblem 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 '(29 + 2x)' equal to zero and attempt to solve: Simplifying 29 + 2x = 0 Solving 29 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 2x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 2x = 0 + -29 2x = 0 + -29 Combine like terms: 0 + -29 = -29 2x = -29 Divide each side by '2'. x = -14.5 Simplifying x = -14.5Solution
x = {0, -14.5}
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