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Simplifying 12x(x + -6) = 2(x + -9) Reorder the terms: 12x(-6 + x) = 2(x + -9) (-6 * 12x + x * 12x) = 2(x + -9) (-72x + 12x2) = 2(x + -9) Reorder the terms: -72x + 12x2 = 2(-9 + x) -72x + 12x2 = (-9 * 2 + x * 2) -72x + 12x2 = (-18 + 2x) Solving -72x + 12x2 = -18 + 2x Solving for variable 'x'. Reorder the terms: 18 + -72x + -2x + 12x2 = -18 + 2x + 18 + -2x Combine like terms: -72x + -2x = -74x 18 + -74x + 12x2 = -18 + 2x + 18 + -2x Reorder the terms: 18 + -74x + 12x2 = -18 + 18 + 2x + -2x Combine like terms: -18 + 18 = 0 18 + -74x + 12x2 = 0 + 2x + -2x 18 + -74x + 12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 18 + -74x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -37x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -37x + 6x2)' equal to zero and attempt to solve: Simplifying 9 + -37x + 6x2 = 0 Solving 9 + -37x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -6.166666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -6.166666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -6.166666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -6.166666667x + x2 = 0 + -1.5 -6.166666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -6.166666667x + x2 = -1.5 The x term is -6.166666667x. Take half its coefficient (-3.083333334). Square it (9.506944449) and add it to both sides. Add '9.506944449' to each side of the equation. -6.166666667x + 9.506944449 + x2 = -1.5 + 9.506944449 Reorder the terms: 9.506944449 + -6.166666667x + x2 = -1.5 + 9.506944449 Combine like terms: -1.5 + 9.506944449 = 8.006944449 9.506944449 + -6.166666667x + x2 = 8.006944449 Factor a perfect square on the left side: (x + -3.083333334)(x + -3.083333334) = 8.006944449 Calculate the square root of the right side: 2.829654475 Break this problem into two subproblems by setting (x + -3.083333334) equal to 2.829654475 and -2.829654475.Subproblem 1
x + -3.083333334 = 2.829654475 Simplifying x + -3.083333334 = 2.829654475 Reorder the terms: -3.083333334 + x = 2.829654475 Solving -3.083333334 + x = 2.829654475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.083333334' to each side of the equation. -3.083333334 + 3.083333334 + x = 2.829654475 + 3.083333334 Combine like terms: -3.083333334 + 3.083333334 = 0.000000000 0.000000000 + x = 2.829654475 + 3.083333334 x = 2.829654475 + 3.083333334 Combine like terms: 2.829654475 + 3.083333334 = 5.912987809 x = 5.912987809 Simplifying x = 5.912987809Subproblem 2
x + -3.083333334 = -2.829654475 Simplifying x + -3.083333334 = -2.829654475 Reorder the terms: -3.083333334 + x = -2.829654475 Solving -3.083333334 + x = -2.829654475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.083333334' to each side of the equation. -3.083333334 + 3.083333334 + x = -2.829654475 + 3.083333334 Combine like terms: -3.083333334 + 3.083333334 = 0.000000000 0.000000000 + x = -2.829654475 + 3.083333334 x = -2.829654475 + 3.083333334 Combine like terms: -2.829654475 + 3.083333334 = 0.253678859 x = 0.253678859 Simplifying x = 0.253678859Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.912987809, 0.253678859}Solution
x = {5.912987809, 0.253678859}
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