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Simplifying x2 + -18x + -60 = 0 Reorder the terms: -60 + -18x + x2 = 0 Solving -60 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -18x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -18x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -18x + x2 = 0 + 60 -18x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -18x + x2 = 60 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 = 60 + 81 Reorder the terms: 81 + -18x + x2 = 60 + 81 Combine like terms: 60 + 81 = 141 81 + -18x + x2 = 141 Factor a perfect square on the left side: (x + -9)(x + -9) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + -9) equal to 11.874342087 and -11.874342087.Subproblem 1
x + -9 = 11.874342087 Simplifying x + -9 = 11.874342087 Reorder the terms: -9 + x = 11.874342087 Solving -9 + x = 11.874342087 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 = 11.874342087 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.874342087 + 9 x = 11.874342087 + 9 Combine like terms: 11.874342087 + 9 = 20.874342087 x = 20.874342087 Simplifying x = 20.874342087Subproblem 2
x + -9 = -11.874342087 Simplifying x + -9 = -11.874342087 Reorder the terms: -9 + x = -11.874342087 Solving -9 + x = -11.874342087 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 = -11.874342087 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.874342087 + 9 x = -11.874342087 + 9 Combine like terms: -11.874342087 + 9 = -2.874342087 x = -2.874342087 Simplifying x = -2.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.874342087, -2.874342087}
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