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Simplifying x2 + -60 = -18x Reorder the terms: -60 + x2 = -18x Solving -60 + x2 = -18x Solving for variable 'x'. Reorder the terms: -60 + 18x + x2 = -18x + 18x Combine like terms: -18x + 18x = 0 -60 + 18x + x2 = 0 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 = 2.874342087 x = 2.874342087 Simplifying x = 2.874342087Subproblem 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 = -20.874342087 x = -20.874342087 Simplifying x = -20.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.874342087, -20.874342087}
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