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Simplifying -6(3x + -11 + -5x) + -4(3x(2x + -2) + -1) = 8x + -12(7x + -4 + -5x) Reorder the terms: -6(-11 + 3x + -5x) + -4(3x(2x + -2) + -1) = 8x + -12(7x + -4 + -5x) Combine like terms: 3x + -5x = -2x -6(-11 + -2x) + -4(3x(2x + -2) + -1) = 8x + -12(7x + -4 + -5x) (-11 * -6 + -2x * -6) + -4(3x(2x + -2) + -1) = 8x + -12(7x + -4 + -5x) (66 + 12x) + -4(3x(2x + -2) + -1) = 8x + -12(7x + -4 + -5x) Reorder the terms: 66 + 12x + -4(3x(-2 + 2x) + -1) = 8x + -12(7x + -4 + -5x) 66 + 12x + -4((-2 * 3x + 2x * 3x) + -1) = 8x + -12(7x + -4 + -5x) 66 + 12x + -4((-6x + 6x2) + -1) = 8x + -12(7x + -4 + -5x) Reorder the terms: 66 + 12x + -4(-1 + -6x + 6x2) = 8x + -12(7x + -4 + -5x) 66 + 12x + (-1 * -4 + -6x * -4 + 6x2 * -4) = 8x + -12(7x + -4 + -5x) 66 + 12x + (4 + 24x + -24x2) = 8x + -12(7x + -4 + -5x) Reorder the terms: 66 + 4 + 12x + 24x + -24x2 = 8x + -12(7x + -4 + -5x) Combine like terms: 66 + 4 = 70 70 + 12x + 24x + -24x2 = 8x + -12(7x + -4 + -5x) Combine like terms: 12x + 24x = 36x 70 + 36x + -24x2 = 8x + -12(7x + -4 + -5x) Reorder the terms: 70 + 36x + -24x2 = 8x + -12(-4 + 7x + -5x) Combine like terms: 7x + -5x = 2x 70 + 36x + -24x2 = 8x + -12(-4 + 2x) 70 + 36x + -24x2 = 8x + (-4 * -12 + 2x * -12) 70 + 36x + -24x2 = 8x + (48 + -24x) Reorder the terms: 70 + 36x + -24x2 = 48 + 8x + -24x Combine like terms: 8x + -24x = -16x 70 + 36x + -24x2 = 48 + -16x Solving 70 + 36x + -24x2 = 48 + -16x Solving for variable 'x'. Reorder the terms: 70 + -48 + 36x + 16x + -24x2 = 48 + -16x + -48 + 16x Combine like terms: 70 + -48 = 22 22 + 36x + 16x + -24x2 = 48 + -16x + -48 + 16x Combine like terms: 36x + 16x = 52x 22 + 52x + -24x2 = 48 + -16x + -48 + 16x Reorder the terms: 22 + 52x + -24x2 = 48 + -48 + -16x + 16x Combine like terms: 48 + -48 = 0 22 + 52x + -24x2 = 0 + -16x + 16x 22 + 52x + -24x2 = -16x + 16x Combine like terms: -16x + 16x = 0 22 + 52x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 26x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 26x + -12x2)' equal to zero and attempt to solve: Simplifying 11 + 26x + -12x2 = 0 Solving 11 + 26x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.9166666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -2.166666667x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -2.166666667x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -2.166666667x + x2 = 0 + 0.9166666667 -2.166666667x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -2.166666667x + x2 = 0.9166666667 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 0.9166666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 0.9166666667 + 1.173611113 Combine like terms: 0.9166666667 + 1.173611113 = 2.0902777797 1.173611113 + -2.166666667x + x2 = 2.0902777797 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 2.0902777797 Calculate the square root of the right side: 1.445779298 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.445779298 and -1.445779298.Subproblem 1
x + -1.083333334 = 1.445779298 Simplifying x + -1.083333334 = 1.445779298 Reorder the terms: -1.083333334 + x = 1.445779298 Solving -1.083333334 + x = 1.445779298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.445779298 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.445779298 + 1.083333334 x = 1.445779298 + 1.083333334 Combine like terms: 1.445779298 + 1.083333334 = 2.529112632 x = 2.529112632 Simplifying x = 2.529112632Subproblem 2
x + -1.083333334 = -1.445779298 Simplifying x + -1.083333334 = -1.445779298 Reorder the terms: -1.083333334 + x = -1.445779298 Solving -1.083333334 + x = -1.445779298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.445779298 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.445779298 + 1.083333334 x = -1.445779298 + 1.083333334 Combine like terms: -1.445779298 + 1.083333334 = -0.362445964 x = -0.362445964 Simplifying x = -0.362445964Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.529112632, -0.362445964}Solution
x = {2.529112632, -0.362445964}
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