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Simplifying x2 + -18x + -106 = 0 Reorder the terms: -106 + -18x + x2 = 0 Solving -106 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + -18x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + -18x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + -18x + x2 = 0 + 106 -18x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 -18x + x2 = 106 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 = 106 + 81 Reorder the terms: 81 + -18x + x2 = 106 + 81 Combine like terms: 106 + 81 = 187 81 + -18x + x2 = 187 Factor a perfect square on the left side: (x + -9)(x + -9) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (x + -9) equal to 13.674794331 and -13.674794331.Subproblem 1
x + -9 = 13.674794331 Simplifying x + -9 = 13.674794331 Reorder the terms: -9 + x = 13.674794331 Solving -9 + x = 13.674794331 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 = 13.674794331 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.674794331 + 9 x = 13.674794331 + 9 Combine like terms: 13.674794331 + 9 = 22.674794331 x = 22.674794331 Simplifying x = 22.674794331Subproblem 2
x + -9 = -13.674794331 Simplifying x + -9 = -13.674794331 Reorder the terms: -9 + x = -13.674794331 Solving -9 + x = -13.674794331 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 = -13.674794331 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.674794331 + 9 x = -13.674794331 + 9 Combine like terms: -13.674794331 + 9 = -4.674794331 x = -4.674794331 Simplifying x = -4.674794331Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.674794331, -4.674794331}
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