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Simplifying 2x2 + 12x = 234 Reorder the terms: 12x + 2x2 = 234 Solving 12x + 2x2 = 234 Solving for variable 'x'. Reorder the terms: -234 + 12x + 2x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-117 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-117 + 6x + x2)' equal to zero and attempt to solve: Simplifying -117 + 6x + x2 = 0 Solving -117 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 6x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + 6x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 6x + x2 = 0 + 117 6x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 6x + x2 = 117 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 117 + 9 Reorder the terms: 9 + 6x + x2 = 117 + 9 Combine like terms: 117 + 9 = 126 9 + 6x + x2 = 126 Factor a perfect square on the left side: (x + 3)(x + 3) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 3) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 3 = 11.22497216 Simplifying x + 3 = 11.22497216 Reorder the terms: 3 + x = 11.22497216 Solving 3 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.22497216 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.22497216 + -3 x = 11.22497216 + -3 Combine like terms: 11.22497216 + -3 = 8.22497216 x = 8.22497216 Simplifying x = 8.22497216Subproblem 2
x + 3 = -11.22497216 Simplifying x + 3 = -11.22497216 Reorder the terms: 3 + x = -11.22497216 Solving 3 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.22497216 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.22497216 + -3 x = -11.22497216 + -3 Combine like terms: -11.22497216 + -3 = -14.22497216 x = -14.22497216 Simplifying x = -14.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.22497216, -14.22497216}Solution
x = {8.22497216, -14.22497216}
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