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Simplifying 2x2 + 12x = 324 Reorder the terms: 12x + 2x2 = 324 Solving 12x + 2x2 = 324 Solving for variable 'x'. Reorder the terms: -324 + 12x + 2x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -324 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-162 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-162 + 6x + x2)' equal to zero and attempt to solve: Simplifying -162 + 6x + x2 = 0 Solving -162 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 6x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + 6x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 6x + x2 = 0 + 162 6x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 6x + x2 = 162 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 = 162 + 9 Reorder the terms: 9 + 6x + x2 = 162 + 9 Combine like terms: 162 + 9 = 171 9 + 6x + x2 = 171 Factor a perfect square on the left side: (x + 3)(x + 3) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 3) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 3 = 13.076696831 Simplifying x + 3 = 13.076696831 Reorder the terms: 3 + x = 13.076696831 Solving 3 + x = 13.076696831 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 = 13.076696831 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.076696831 + -3 x = 13.076696831 + -3 Combine like terms: 13.076696831 + -3 = 10.076696831 x = 10.076696831 Simplifying x = 10.076696831Subproblem 2
x + 3 = -13.076696831 Simplifying x + 3 = -13.076696831 Reorder the terms: 3 + x = -13.076696831 Solving 3 + x = -13.076696831 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 = -13.076696831 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.076696831 + -3 x = -13.076696831 + -3 Combine like terms: -13.076696831 + -3 = -16.076696831 x = -16.076696831 Simplifying x = -16.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.076696831, -16.076696831}Solution
x = {10.076696831, -16.076696831}
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