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Simplifying x2 + -18x + -162 = 0 Reorder the terms: -162 + -18x + x2 = 0 Solving -162 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + -18x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + -18x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + -18x + x2 = 0 + 162 -18x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 -18x + x2 = 162 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 = 162 + 81 Reorder the terms: 81 + -18x + x2 = 162 + 81 Combine like terms: 162 + 81 = 243 81 + -18x + x2 = 243 Factor a perfect square on the left side: (x + -9)(x + -9) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (x + -9) equal to 15.588457268 and -15.588457268.Subproblem 1
x + -9 = 15.588457268 Simplifying x + -9 = 15.588457268 Reorder the terms: -9 + x = 15.588457268 Solving -9 + x = 15.588457268 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 = 15.588457268 + 9 Combine like terms: -9 + 9 = 0 0 + x = 15.588457268 + 9 x = 15.588457268 + 9 Combine like terms: 15.588457268 + 9 = 24.588457268 x = 24.588457268 Simplifying x = 24.588457268Subproblem 2
x + -9 = -15.588457268 Simplifying x + -9 = -15.588457268 Reorder the terms: -9 + x = -15.588457268 Solving -9 + x = -15.588457268 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 = -15.588457268 + 9 Combine like terms: -9 + 9 = 0 0 + x = -15.588457268 + 9 x = -15.588457268 + 9 Combine like terms: -15.588457268 + 9 = -6.588457268 x = -6.588457268 Simplifying x = -6.588457268Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.588457268, -6.588457268}
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