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Simplifying 7710 = 63x + x2 Solving 7710 = 63x + x2 Solving for variable 'x'. Reorder the terms: 7710 + -63x + -1x2 = 63x + -63x + x2 + -1x2 Combine like terms: 63x + -63x = 0 7710 + -63x + -1x2 = 0 + x2 + -1x2 7710 + -63x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7710 + -63x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7710 + 63x + x2 = 0 Move the constant term to the right: Add '7710' to each side of the equation. -7710 + 63x + 7710 + x2 = 0 + 7710 Reorder the terms: -7710 + 7710 + 63x + x2 = 0 + 7710 Combine like terms: -7710 + 7710 = 0 0 + 63x + x2 = 0 + 7710 63x + x2 = 0 + 7710 Combine like terms: 0 + 7710 = 7710 63x + x2 = 7710 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = 7710 + 992.25 Reorder the terms: 992.25 + 63x + x2 = 7710 + 992.25 Combine like terms: 7710 + 992.25 = 8702.25 992.25 + 63x + x2 = 8702.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 8702.25 Calculate the square root of the right side: 93.285851017 Break this problem into two subproblems by setting (x + 31.5) equal to 93.285851017 and -93.285851017.Subproblem 1
x + 31.5 = 93.285851017 Simplifying x + 31.5 = 93.285851017 Reorder the terms: 31.5 + x = 93.285851017 Solving 31.5 + x = 93.285851017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 93.285851017 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 93.285851017 + -31.5 x = 93.285851017 + -31.5 Combine like terms: 93.285851017 + -31.5 = 61.785851017 x = 61.785851017 Simplifying x = 61.785851017Subproblem 2
x + 31.5 = -93.285851017 Simplifying x + 31.5 = -93.285851017 Reorder the terms: 31.5 + x = -93.285851017 Solving 31.5 + x = -93.285851017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -93.285851017 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -93.285851017 + -31.5 x = -93.285851017 + -31.5 Combine like terms: -93.285851017 + -31.5 = -124.785851017 x = -124.785851017 Simplifying x = -124.785851017Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.785851017, -124.785851017}
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