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Simplifying 2500 + -2x2 + -1x = 0 Reorder the terms: 2500 + -1x + -2x2 = 0 Solving 2500 + -1x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1250 + 0.5x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + 0.5x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + 0.5x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + 0.5x + x2 = 0 + 1250 0.5x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 0.5x + x2 = 1250 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1250 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1250 + 0.0625 Combine like terms: 1250 + 0.0625 = 1250.0625 0.0625 + 0.5x + x2 = 1250.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1250.0625 Calculate the square root of the right side: 35.356222932 Break this problem into two subproblems by setting (x + 0.25) equal to 35.356222932 and -35.356222932.Subproblem 1
x + 0.25 = 35.356222932 Simplifying x + 0.25 = 35.356222932 Reorder the terms: 0.25 + x = 35.356222932 Solving 0.25 + x = 35.356222932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 35.356222932 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 35.356222932 + -0.25 x = 35.356222932 + -0.25 Combine like terms: 35.356222932 + -0.25 = 35.106222932 x = 35.106222932 Simplifying x = 35.106222932Subproblem 2
x + 0.25 = -35.356222932 Simplifying x + 0.25 = -35.356222932 Reorder the terms: 0.25 + x = -35.356222932 Solving 0.25 + x = -35.356222932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -35.356222932 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -35.356222932 + -0.25 x = -35.356222932 + -0.25 Combine like terms: -35.356222932 + -0.25 = -35.606222932 x = -35.606222932 Simplifying x = -35.606222932Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.106222932, -35.606222932}
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