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Simplifying 6x2 + -6x + -12 = 69 Reorder the terms: -12 + -6x + 6x2 = 69 Solving -12 + -6x + 6x2 = 69 Solving for variable 'x'. Reorder the terms: -12 + -69 + -6x + 6x2 = 69 + -69 Combine like terms: -12 + -69 = -81 -81 + -6x + 6x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -81 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + -2x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -27 + -2x + 2x2 = 0 Solving -27 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -1x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -1x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -1x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -1x + x2 = 0 + 13.5 -1x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -1x + x2 = 13.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 13.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 13.5 + 0.25 Combine like terms: 13.5 + 0.25 = 13.75 0.25 + -1x + x2 = 13.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + -0.5) equal to 3.708099244 and -3.708099244.Subproblem 1
x + -0.5 = 3.708099244 Simplifying x + -0.5 = 3.708099244 Reorder the terms: -0.5 + x = 3.708099244 Solving -0.5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.708099244 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.708099244 + 0.5 x = 3.708099244 + 0.5 Combine like terms: 3.708099244 + 0.5 = 4.208099244 x = 4.208099244 Simplifying x = 4.208099244Subproblem 2
x + -0.5 = -3.708099244 Simplifying x + -0.5 = -3.708099244 Reorder the terms: -0.5 + x = -3.708099244 Solving -0.5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.708099244 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.708099244 + 0.5 x = -3.708099244 + 0.5 Combine like terms: -3.708099244 + 0.5 = -3.208099244 x = -3.208099244 Simplifying x = -3.208099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.208099244, -3.208099244}Solution
x = {4.208099244, -3.208099244}
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