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Simplifying 0 = x2 + -8x + -60 Reorder the terms: 0 = -60 + -8x + x2 Solving 0 = -60 + -8x + x2 Solving for variable 'x'. Combine like terms: 0 + 60 = 60 60 + 8x + -1x2 = -60 + -8x + x2 + 60 + 8x + -1x2 Reorder the terms: 60 + 8x + -1x2 = -60 + 60 + -8x + 8x + x2 + -1x2 Combine like terms: -60 + 60 = 0 60 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2 60 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 60 + 8x + -1x2 = 0 + x2 + -1x2 60 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -8x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -8x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -8x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -8x + x2 = 0 + 60 -8x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -8x + x2 = 60 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 60 + 16 Reorder the terms: 16 + -8x + x2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + -8x + x2 = 76 Factor a perfect square on the left side: (x + -4)(x + -4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -4) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -4 = 8.717797887 Simplifying x + -4 = 8.717797887 Reorder the terms: -4 + x = 8.717797887 Solving -4 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.717797887 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.717797887 + 4 x = 8.717797887 + 4 Combine like terms: 8.717797887 + 4 = 12.717797887 x = 12.717797887 Simplifying x = 12.717797887Subproblem 2
x + -4 = -8.717797887 Simplifying x + -4 = -8.717797887 Reorder the terms: -4 + x = -8.717797887 Solving -4 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.717797887 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.717797887 + 4 x = -8.717797887 + 4 Combine like terms: -8.717797887 + 4 = -4.717797887 x = -4.717797887 Simplifying x = -4.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.717797887, -4.717797887}
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