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Simplifying x + 4 = x2 + -16x + 60 Reorder the terms: 4 + x = x2 + -16x + 60 Reorder the terms: 4 + x = 60 + -16x + x2 Solving 4 + x = 60 + -16x + x2 Solving for variable 'x'. Reorder the terms: 4 + -60 + x + 16x + -1x2 = 60 + -16x + x2 + -60 + 16x + -1x2 Combine like terms: 4 + -60 = -56 -56 + x + 16x + -1x2 = 60 + -16x + x2 + -60 + 16x + -1x2 Combine like terms: x + 16x = 17x -56 + 17x + -1x2 = 60 + -16x + x2 + -60 + 16x + -1x2 Reorder the terms: -56 + 17x + -1x2 = 60 + -60 + -16x + 16x + x2 + -1x2 Combine like terms: 60 + -60 = 0 -56 + 17x + -1x2 = 0 + -16x + 16x + x2 + -1x2 -56 + 17x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 -56 + 17x + -1x2 = 0 + x2 + -1x2 -56 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -56 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 56 + -17x + x2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -17x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -17x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -17x + x2 = 0 + -56 -17x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -17x + x2 = -56 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -56 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -56 + 72.25 Combine like terms: -56 + 72.25 = 16.25 72.25 + -17x + x2 = 16.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -8.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -8.5 = 4.031128874 Simplifying x + -8.5 = 4.031128874 Reorder the terms: -8.5 + x = 4.031128874 Solving -8.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 4.031128874 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.031128874 + 8.5 x = 4.031128874 + 8.5 Combine like terms: 4.031128874 + 8.5 = 12.531128874 x = 12.531128874 Simplifying x = 12.531128874Subproblem 2
x + -8.5 = -4.031128874 Simplifying x + -8.5 = -4.031128874 Reorder the terms: -8.5 + x = -4.031128874 Solving -8.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -4.031128874 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.031128874 + 8.5 x = -4.031128874 + 8.5 Combine like terms: -4.031128874 + 8.5 = 4.468871126 x = 4.468871126 Simplifying x = 4.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.531128874, 4.468871126}
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