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Simplifying x2 + -18x + -108 = 0 Reorder the terms: -108 + -18x + x2 = 0 Solving -108 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -18x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -18x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -18x + x2 = 0 + 108 -18x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -18x + x2 = 108 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 = 108 + 81 Reorder the terms: 81 + -18x + x2 = 108 + 81 Combine like terms: 108 + 81 = 189 81 + -18x + x2 = 189 Factor a perfect square on the left side: (x + -9)(x + -9) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + -9) equal to 13.747727085 and -13.747727085.Subproblem 1
x + -9 = 13.747727085 Simplifying x + -9 = 13.747727085 Reorder the terms: -9 + x = 13.747727085 Solving -9 + x = 13.747727085 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 = 13.747727085 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.747727085 + 9 x = 13.747727085 + 9 Combine like terms: 13.747727085 + 9 = 22.747727085 x = 22.747727085 Simplifying x = 22.747727085Subproblem 2
x + -9 = -13.747727085 Simplifying x + -9 = -13.747727085 Reorder the terms: -9 + x = -13.747727085 Solving -9 + x = -13.747727085 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 = -13.747727085 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.747727085 + 9 x = -13.747727085 + 9 Combine like terms: -13.747727085 + 9 = -4.747727085 x = -4.747727085 Simplifying x = -4.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.747727085, -4.747727085}
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