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Simplifying 3(x + -12) = 2x(x + 17) Reorder the terms: 3(-12 + x) = 2x(x + 17) (-12 * 3 + x * 3) = 2x(x + 17) (-36 + 3x) = 2x(x + 17) Reorder the terms: -36 + 3x = 2x(17 + x) -36 + 3x = (17 * 2x + x * 2x) -36 + 3x = (34x + 2x2) Solving -36 + 3x = 34x + 2x2 Solving for variable 'x'. Combine like terms: 3x + -34x = -31x -36 + -31x + -2x2 = 34x + 2x2 + -34x + -2x2 Reorder the terms: -36 + -31x + -2x2 = 34x + -34x + 2x2 + -2x2 Combine like terms: 34x + -34x = 0 -36 + -31x + -2x2 = 0 + 2x2 + -2x2 -36 + -31x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -36 + -31x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 31x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(36 + 31x + 2x2)' equal to zero and attempt to solve: Simplifying 36 + 31x + 2x2 = 0 Solving 36 + 31x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + 15.5x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + 15.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 15.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 15.5x + x2 = 0 + -18 15.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 15.5x + x2 = -18 The x term is 15.5x. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5x + 60.0625 + x2 = -18 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = -18 + 60.0625 Combine like terms: -18 + 60.0625 = 42.0625 60.0625 + 15.5x + x2 = 42.0625 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 42.0625 Calculate the square root of the right side: 6.485560886 Break this problem into two subproblems by setting (x + 7.75) equal to 6.485560886 and -6.485560886.Subproblem 1
x + 7.75 = 6.485560886 Simplifying x + 7.75 = 6.485560886 Reorder the terms: 7.75 + x = 6.485560886 Solving 7.75 + x = 6.485560886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 6.485560886 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 6.485560886 + -7.75 x = 6.485560886 + -7.75 Combine like terms: 6.485560886 + -7.75 = -1.264439114 x = -1.264439114 Simplifying x = -1.264439114Subproblem 2
x + 7.75 = -6.485560886 Simplifying x + 7.75 = -6.485560886 Reorder the terms: 7.75 + x = -6.485560886 Solving 7.75 + x = -6.485560886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -6.485560886 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -6.485560886 + -7.75 x = -6.485560886 + -7.75 Combine like terms: -6.485560886 + -7.75 = -14.235560886 x = -14.235560886 Simplifying x = -14.235560886Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.264439114, -14.235560886}Solution
x = {-1.264439114, -14.235560886}
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