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Simplifying 10(x + -2) + 19 = (5x + -1)(1 + 4x) Reorder the terms: 10(-2 + x) + 19 = (5x + -1)(1 + 4x) (-2 * 10 + x * 10) + 19 = (5x + -1)(1 + 4x) (-20 + 10x) + 19 = (5x + -1)(1 + 4x) Reorder the terms: -20 + 19 + 10x = (5x + -1)(1 + 4x) Combine like terms: -20 + 19 = -1 -1 + 10x = (5x + -1)(1 + 4x) Reorder the terms: -1 + 10x = (-1 + 5x)(1 + 4x) Multiply (-1 + 5x) * (1 + 4x) -1 + 10x = (-1(1 + 4x) + 5x * (1 + 4x)) -1 + 10x = ((1 * -1 + 4x * -1) + 5x * (1 + 4x)) -1 + 10x = ((-1 + -4x) + 5x * (1 + 4x)) -1 + 10x = (-1 + -4x + (1 * 5x + 4x * 5x)) -1 + 10x = (-1 + -4x + (5x + 20x2)) Combine like terms: -4x + 5x = 1x -1 + 10x = (-1 + 1x + 20x2) Add '1' to each side of the equation. -1 + 1 + 10x = -1 + 1x + 1 + 20x2 Combine like terms: -1 + 1 = 0 0 + 10x = -1 + 1x + 1 + 20x2 10x = -1 + 1x + 1 + 20x2 Reorder the terms: 10x = -1 + 1 + 1x + 20x2 Combine like terms: -1 + 1 = 0 10x = 0 + 1x + 20x2 10x = 1x + 20x2 Solving 10x = 1x + 20x2 Solving for variable 'x'. Combine like terms: 10x + -1x = 9x 9x + -20x2 = 1x + 20x2 + -1x + -20x2 Reorder the terms: 9x + -20x2 = 1x + -1x + 20x2 + -20x2 Combine like terms: 1x + -1x = 0 9x + -20x2 = 0 + 20x2 + -20x2 9x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 9x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(9 + -20x) = 0Subproblem 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 '(9 + -20x)' equal to zero and attempt to solve: Simplifying 9 + -20x = 0 Solving 9 + -20x = 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 + -20x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -20x = 0 + -9 -20x = 0 + -9 Combine like terms: 0 + -9 = -9 -20x = -9 Divide each side by '-20'. x = 0.45 Simplifying x = 0.45Solution
x = {0, 0.45}
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