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Simplifying 5x + x2 + x2 = 625 Combine like terms: x2 + x2 = 2x2 5x + 2x2 = 625 Solving 5x + 2x2 = 625 Solving for variable 'x'. Reorder the terms: -625 + 5x + 2x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -312.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '312.5' to each side of the equation. -312.5 + 2.5x + 312.5 + x2 = 0 + 312.5 Reorder the terms: -312.5 + 312.5 + 2.5x + x2 = 0 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + 2.5x + x2 = 0 + 312.5 2.5x + x2 = 0 + 312.5 Combine like terms: 0 + 312.5 = 312.5 2.5x + x2 = 312.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 312.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 312.5 + 1.5625 Combine like terms: 312.5 + 1.5625 = 314.0625 1.5625 + 2.5x + x2 = 314.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 314.0625 Calculate the square root of the right side: 17.721808598 Break this problem into two subproblems by setting (x + 1.25) equal to 17.721808598 and -17.721808598.Subproblem 1
x + 1.25 = 17.721808598 Simplifying x + 1.25 = 17.721808598 Reorder the terms: 1.25 + x = 17.721808598 Solving 1.25 + x = 17.721808598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 17.721808598 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 17.721808598 + -1.25 x = 17.721808598 + -1.25 Combine like terms: 17.721808598 + -1.25 = 16.471808598 x = 16.471808598 Simplifying x = 16.471808598Subproblem 2
x + 1.25 = -17.721808598 Simplifying x + 1.25 = -17.721808598 Reorder the terms: 1.25 + x = -17.721808598 Solving 1.25 + x = -17.721808598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -17.721808598 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -17.721808598 + -1.25 x = -17.721808598 + -1.25 Combine like terms: -17.721808598 + -1.25 = -18.971808598 x = -18.971808598 Simplifying x = -18.971808598Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.471808598, -18.971808598}
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