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Simplifying 5x + 2(2x + 3) = (x + -8)(10x + -3) Reorder the terms: 5x + 2(3 + 2x) = (x + -8)(10x + -3) 5x + (3 * 2 + 2x * 2) = (x + -8)(10x + -3) 5x + (6 + 4x) = (x + -8)(10x + -3) Reorder the terms: 6 + 5x + 4x = (x + -8)(10x + -3) Combine like terms: 5x + 4x = 9x 6 + 9x = (x + -8)(10x + -3) Reorder the terms: 6 + 9x = (-8 + x)(10x + -3) Reorder the terms: 6 + 9x = (-8 + x)(-3 + 10x) Multiply (-8 + x) * (-3 + 10x) 6 + 9x = (-8(-3 + 10x) + x(-3 + 10x)) 6 + 9x = ((-3 * -8 + 10x * -8) + x(-3 + 10x)) 6 + 9x = ((24 + -80x) + x(-3 + 10x)) 6 + 9x = (24 + -80x + (-3 * x + 10x * x)) 6 + 9x = (24 + -80x + (-3x + 10x2)) Combine like terms: -80x + -3x = -83x 6 + 9x = (24 + -83x + 10x2) Solving 6 + 9x = 24 + -83x + 10x2 Solving for variable 'x'. Reorder the terms: 6 + -24 + 9x + 83x + -10x2 = 24 + -83x + 10x2 + -24 + 83x + -10x2 Combine like terms: 6 + -24 = -18 -18 + 9x + 83x + -10x2 = 24 + -83x + 10x2 + -24 + 83x + -10x2 Combine like terms: 9x + 83x = 92x -18 + 92x + -10x2 = 24 + -83x + 10x2 + -24 + 83x + -10x2 Reorder the terms: -18 + 92x + -10x2 = 24 + -24 + -83x + 83x + 10x2 + -10x2 Combine like terms: 24 + -24 = 0 -18 + 92x + -10x2 = 0 + -83x + 83x + 10x2 + -10x2 -18 + 92x + -10x2 = -83x + 83x + 10x2 + -10x2 Combine like terms: -83x + 83x = 0 -18 + 92x + -10x2 = 0 + 10x2 + -10x2 -18 + 92x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -18 + 92x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 46x + -5x2) = 0 Factor a trinomial. 2((-9 + x)(1 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {9, 0.2}
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