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Simplifying 3(x + -3) + -1(5 + -27x) = (8x + -7)(-2x + 9) Reorder the terms: 3(-3 + x) + -1(5 + -27x) = (8x + -7)(-2x + 9) (-3 * 3 + x * 3) + -1(5 + -27x) = (8x + -7)(-2x + 9) (-9 + 3x) + -1(5 + -27x) = (8x + -7)(-2x + 9) -9 + 3x + (5 * -1 + -27x * -1) = (8x + -7)(-2x + 9) -9 + 3x + (-5 + 27x) = (8x + -7)(-2x + 9) Reorder the terms: -9 + -5 + 3x + 27x = (8x + -7)(-2x + 9) Combine like terms: -9 + -5 = -14 -14 + 3x + 27x = (8x + -7)(-2x + 9) Combine like terms: 3x + 27x = 30x -14 + 30x = (8x + -7)(-2x + 9) Reorder the terms: -14 + 30x = (-7 + 8x)(-2x + 9) Reorder the terms: -14 + 30x = (-7 + 8x)(9 + -2x) Multiply (-7 + 8x) * (9 + -2x) -14 + 30x = (-7(9 + -2x) + 8x * (9 + -2x)) -14 + 30x = ((9 * -7 + -2x * -7) + 8x * (9 + -2x)) -14 + 30x = ((-63 + 14x) + 8x * (9 + -2x)) -14 + 30x = (-63 + 14x + (9 * 8x + -2x * 8x)) -14 + 30x = (-63 + 14x + (72x + -16x2)) Combine like terms: 14x + 72x = 86x -14 + 30x = (-63 + 86x + -16x2) Solving -14 + 30x = -63 + 86x + -16x2 Solving for variable 'x'. Reorder the terms: -14 + 63 + 30x + -86x + 16x2 = -63 + 86x + -16x2 + 63 + -86x + 16x2 Combine like terms: -14 + 63 = 49 49 + 30x + -86x + 16x2 = -63 + 86x + -16x2 + 63 + -86x + 16x2 Combine like terms: 30x + -86x = -56x 49 + -56x + 16x2 = -63 + 86x + -16x2 + 63 + -86x + 16x2 Reorder the terms: 49 + -56x + 16x2 = -63 + 63 + 86x + -86x + -16x2 + 16x2 Combine like terms: -63 + 63 = 0 49 + -56x + 16x2 = 0 + 86x + -86x + -16x2 + 16x2 49 + -56x + 16x2 = 86x + -86x + -16x2 + 16x2 Combine like terms: 86x + -86x = 0 49 + -56x + 16x2 = 0 + -16x2 + 16x2 49 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 49 + -56x + 16x2 = 0 Factor a trinomial. (7 + -4x)(7 + -4x) = 0Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {1.75, 1.75}
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