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Simplifying 2x2 + 5x = 125 Reorder the terms: 5x + 2x2 = 125 Solving 5x + 2x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 5x + 2x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + 2.5x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + 2.5x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + 2.5x + x2 = 0 + 62.5 2.5x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 2.5x + x2 = 62.5 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 = 62.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 62.5 + 1.5625 Combine like terms: 62.5 + 1.5625 = 64.0625 1.5625 + 2.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + 1.25) equal to 8.003905297 and -8.003905297.Subproblem 1
x + 1.25 = 8.003905297 Simplifying x + 1.25 = 8.003905297 Reorder the terms: 1.25 + x = 8.003905297 Solving 1.25 + x = 8.003905297 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 = 8.003905297 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.003905297 + -1.25 x = 8.003905297 + -1.25 Combine like terms: 8.003905297 + -1.25 = 6.753905297 x = 6.753905297 Simplifying x = 6.753905297Subproblem 2
x + 1.25 = -8.003905297 Simplifying x + 1.25 = -8.003905297 Reorder the terms: 1.25 + x = -8.003905297 Solving 1.25 + x = -8.003905297 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 = -8.003905297 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.003905297 + -1.25 x = -8.003905297 + -1.25 Combine like terms: -8.003905297 + -1.25 = -9.253905297 x = -9.253905297 Simplifying x = -9.253905297Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.753905297, -9.253905297}
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