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Simplifying 2x2 + 36x + 12 = 0 Reorder the terms: 12 + 36x + 2x2 = 0 Solving 12 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 18x + x2)' equal to zero and attempt to solve: Simplifying 6 + 18x + x2 = 0 Solving 6 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 18x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 18x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 18x + x2 = 0 + -6 18x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 18x + x2 = -6 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -6 + 81 Reorder the terms: 81 + 18x + x2 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + 18x + x2 = 75 Factor a perfect square on the left side: (x + 9)(x + 9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 9) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 9 = 8.660254038 Simplifying x + 9 = 8.660254038 Reorder the terms: 9 + x = 8.660254038 Solving 9 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 8.660254038 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.660254038 + -9 x = 8.660254038 + -9 Combine like terms: 8.660254038 + -9 = -0.339745962 x = -0.339745962 Simplifying x = -0.339745962Subproblem 2
x + 9 = -8.660254038 Simplifying x + 9 = -8.660254038 Reorder the terms: 9 + x = -8.660254038 Solving 9 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -8.660254038 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.660254038 + -9 x = -8.660254038 + -9 Combine like terms: -8.660254038 + -9 = -17.660254038 x = -17.660254038 Simplifying x = -17.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.339745962, -17.660254038}Solution
x = {-0.339745962, -17.660254038}
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