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Simplifying 2x2 + -36x + -6 = 0 Reorder the terms: -6 + -36x + 2x2 = 0 Solving -6 + -36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -18x + x2)' equal to zero and attempt to solve: Simplifying -3 + -18x + x2 = 0 Solving -3 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -18x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -18x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -18x + x2 = 0 + 3 -18x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -18x + x2 = 3 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 = 3 + 81 Reorder the terms: 81 + -18x + x2 = 3 + 81 Combine like terms: 3 + 81 = 84 81 + -18x + x2 = 84 Factor a perfect square on the left side: (x + -9)(x + -9) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -9) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -9 = 9.16515139 Simplifying x + -9 = 9.16515139 Reorder the terms: -9 + x = 9.16515139 Solving -9 + x = 9.16515139 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 = 9.16515139 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.16515139 + 9 x = 9.16515139 + 9 Combine like terms: 9.16515139 + 9 = 18.16515139 x = 18.16515139 Simplifying x = 18.16515139Subproblem 2
x + -9 = -9.16515139 Simplifying x + -9 = -9.16515139 Reorder the terms: -9 + x = -9.16515139 Solving -9 + x = -9.16515139 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 = -9.16515139 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.16515139 + 9 x = -9.16515139 + 9 Combine like terms: -9.16515139 + 9 = -0.16515139 x = -0.16515139 Simplifying x = -0.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.16515139, -0.16515139}Solution
x = {18.16515139, -0.16515139}
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