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Simplifying 100(x + -2) + 64(x + 2) + -9(x + 2)(x + -2) = 0 Reorder the terms: 100(-2 + x) + 64(x + 2) + -9(x + 2)(x + -2) = 0 (-2 * 100 + x * 100) + 64(x + 2) + -9(x + 2)(x + -2) = 0 (-200 + 100x) + 64(x + 2) + -9(x + 2)(x + -2) = 0 Reorder the terms: -200 + 100x + 64(2 + x) + -9(x + 2)(x + -2) = 0 -200 + 100x + (2 * 64 + x * 64) + -9(x + 2)(x + -2) = 0 -200 + 100x + (128 + 64x) + -9(x + 2)(x + -2) = 0 Reorder the terms: -200 + 100x + 128 + 64x + -9(2 + x)(x + -2) = 0 Reorder the terms: -200 + 100x + 128 + 64x + -9(2 + x)(-2 + x) = 0 Multiply (2 + x) * (-2 + x) -200 + 100x + 128 + 64x + -9(2(-2 + x) + x(-2 + x)) = 0 -200 + 100x + 128 + 64x + -9((-2 * 2 + x * 2) + x(-2 + x)) = 0 -200 + 100x + 128 + 64x + -9((-4 + 2x) + x(-2 + x)) = 0 -200 + 100x + 128 + 64x + -9(-4 + 2x + (-2 * x + x * x)) = 0 -200 + 100x + 128 + 64x + -9(-4 + 2x + (-2x + x2)) = 0 Combine like terms: 2x + -2x = 0 -200 + 100x + 128 + 64x + -9(-4 + 0 + x2) = 0 -200 + 100x + 128 + 64x + -9(-4 + x2) = 0 -200 + 100x + 128 + 64x + (-4 * -9 + x2 * -9) = 0 -200 + 100x + 128 + 64x + (36 + -9x2) = 0 Reorder the terms: -200 + 128 + 36 + 100x + 64x + -9x2 = 0 Combine like terms: -200 + 128 = -72 -72 + 36 + 100x + 64x + -9x2 = 0 Combine like terms: -72 + 36 = -36 -36 + 100x + 64x + -9x2 = 0 Combine like terms: 100x + 64x = 164x -36 + 164x + -9x2 = 0 Solving -36 + 164x + -9x2 = 0 Solving for variable 'x'. Factor a trinomial. (-18 + x)(2 + -9x) = 0Subproblem 1
Set the factor '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Simplifying x = 18Subproblem 2
Set the factor '(2 + -9x)' equal to zero and attempt to solve: Simplifying 2 + -9x = 0 Solving 2 + -9x = 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 + -9x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9x = 0 + -2 -9x = 0 + -2 Combine like terms: 0 + -2 = -2 -9x = -2 Divide each side by '-9'. x = 0.2222222222 Simplifying x = 0.2222222222Solution
x = {18, 0.2222222222}
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