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Simplifying x2 + -18x + -90 = 0 Reorder the terms: -90 + -18x + x2 = 0 Solving -90 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -18x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -18x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -18x + x2 = 0 + 90 -18x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -18x + x2 = 90 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 = 90 + 81 Reorder the terms: 81 + -18x + x2 = 90 + 81 Combine like terms: 90 + 81 = 171 81 + -18x + x2 = 171 Factor a perfect square on the left side: (x + -9)(x + -9) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + -9) equal to 13.076696831 and -13.076696831.Subproblem 1
x + -9 = 13.076696831 Simplifying x + -9 = 13.076696831 Reorder the terms: -9 + x = 13.076696831 Solving -9 + x = 13.076696831 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 = 13.076696831 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.076696831 + 9 x = 13.076696831 + 9 Combine like terms: 13.076696831 + 9 = 22.076696831 x = 22.076696831 Simplifying x = 22.076696831Subproblem 2
x + -9 = -13.076696831 Simplifying x + -9 = -13.076696831 Reorder the terms: -9 + x = -13.076696831 Solving -9 + x = -13.076696831 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 = -13.076696831 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.076696831 + 9 x = -13.076696831 + 9 Combine like terms: -13.076696831 + 9 = -4.076696831 x = -4.076696831 Simplifying x = -4.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.076696831, -4.076696831}
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