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Simplifying 250 = x + 2x2 Solving 250 = x + 2x2 Solving for variable 'x'. Reorder the terms: 250 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 250 + -1x + -2x2 = 0 + 2x2 + -2x2 250 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 250 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -125 + 0.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 0.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 0.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 0.5x + x2 = 0 + 125 0.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 0.5x + x2 = 125 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 = 125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 125 + 0.0625 Combine like terms: 125 + 0.0625 = 125.0625 0.0625 + 0.5x + x2 = 125.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 125.0625 Calculate the square root of the right side: 11.183134623 Break this problem into two subproblems by setting (x + 0.25) equal to 11.183134623 and -11.183134623.Subproblem 1
x + 0.25 = 11.183134623 Simplifying x + 0.25 = 11.183134623 Reorder the terms: 0.25 + x = 11.183134623 Solving 0.25 + x = 11.183134623 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 = 11.183134623 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 11.183134623 + -0.25 x = 11.183134623 + -0.25 Combine like terms: 11.183134623 + -0.25 = 10.933134623 x = 10.933134623 Simplifying x = 10.933134623Subproblem 2
x + 0.25 = -11.183134623 Simplifying x + 0.25 = -11.183134623 Reorder the terms: 0.25 + x = -11.183134623 Solving 0.25 + x = -11.183134623 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 = -11.183134623 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -11.183134623 + -0.25 x = -11.183134623 + -0.25 Combine like terms: -11.183134623 + -0.25 = -11.433134623 x = -11.433134623 Simplifying x = -11.433134623Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.933134623, -11.433134623}
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