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Simplifying 4(9x + -7) = 2x(1 + 5x) + -1(1 + -1x) Reorder the terms: 4(-7 + 9x) = 2x(1 + 5x) + -1(1 + -1x) (-7 * 4 + 9x * 4) = 2x(1 + 5x) + -1(1 + -1x) (-28 + 36x) = 2x(1 + 5x) + -1(1 + -1x) -28 + 36x = (1 * 2x + 5x * 2x) + -1(1 + -1x) -28 + 36x = (2x + 10x2) + -1(1 + -1x) -28 + 36x = 2x + 10x2 + (1 * -1 + -1x * -1) -28 + 36x = 2x + 10x2 + (-1 + 1x) Reorder the terms: -28 + 36x = -1 + 2x + 1x + 10x2 Combine like terms: 2x + 1x = 3x -28 + 36x = -1 + 3x + 10x2 Solving -28 + 36x = -1 + 3x + 10x2 Solving for variable 'x'. Reorder the terms: -28 + 1 + 36x + -3x + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2 Combine like terms: -28 + 1 = -27 -27 + 36x + -3x + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2 Combine like terms: 36x + -3x = 33x -27 + 33x + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2 Reorder the terms: -27 + 33x + -10x2 = -1 + 1 + 3x + -3x + 10x2 + -10x2 Combine like terms: -1 + 1 = 0 -27 + 33x + -10x2 = 0 + 3x + -3x + 10x2 + -10x2 -27 + 33x + -10x2 = 3x + -3x + 10x2 + -10x2 Combine like terms: 3x + -3x = 0 -27 + 33x + -10x2 = 0 + 10x2 + -10x2 -27 + 33x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -27 + 33x + -10x2 = 0 Factor a trinomial. (-9 + 5x)(3 + -2x) = 0Subproblem 1
Set the factor '(-9 + 5x)' equal to zero and attempt to solve: Simplifying -9 + 5x = 0 Solving -9 + 5x = 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 + 5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5x = 0 + 9 5x = 0 + 9 Combine like terms: 0 + 9 = 9 5x = 9 Divide each side by '5'. x = 1.8 Simplifying x = 1.8Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {1.8, 1.5}
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