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Simplifying 25000 = 0.5x2 + 11x Reorder the terms: 25000 = 11x + 0.5x2 Solving 25000 = 11x + 0.5x2 Solving for variable 'x'. Reorder the terms: 25000 + -11x + -0.5x2 = 11x + -11x + 0.5x2 + -0.5x2 Combine like terms: 11x + -11x = 0 25000 + -11x + -0.5x2 = 0 + 0.5x2 + -0.5x2 25000 + -11x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 25000 + -11x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -50000 + 22x + x2 = 0 Move the constant term to the right: Add '50000' to each side of the equation. -50000 + 22x + 50000 + x2 = 0 + 50000 Reorder the terms: -50000 + 50000 + 22x + x2 = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + 22x + x2 = 0 + 50000 22x + x2 = 0 + 50000 Combine like terms: 0 + 50000 = 50000 22x + x2 = 50000 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 50000 + 121 Reorder the terms: 121 + 22x + x2 = 50000 + 121 Combine like terms: 50000 + 121 = 50121 121 + 22x + x2 = 50121 Factor a perfect square on the left side: (x + 11)(x + 11) = 50121 Calculate the square root of the right side: 223.877198482 Break this problem into two subproblems by setting (x + 11) equal to 223.877198482 and -223.877198482.Subproblem 1
x + 11 = 223.877198482 Simplifying x + 11 = 223.877198482 Reorder the terms: 11 + x = 223.877198482 Solving 11 + x = 223.877198482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 223.877198482 + -11 Combine like terms: 11 + -11 = 0 0 + x = 223.877198482 + -11 x = 223.877198482 + -11 Combine like terms: 223.877198482 + -11 = 212.877198482 x = 212.877198482 Simplifying x = 212.877198482Subproblem 2
x + 11 = -223.877198482 Simplifying x + 11 = -223.877198482 Reorder the terms: 11 + x = -223.877198482 Solving 11 + x = -223.877198482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -223.877198482 + -11 Combine like terms: 11 + -11 = 0 0 + x = -223.877198482 + -11 x = -223.877198482 + -11 Combine like terms: -223.877198482 + -11 = -234.877198482 x = -234.877198482 Simplifying x = -234.877198482Solution
The solution to the problem is based on the solutions from the subproblems. x = {212.877198482, -234.877198482}
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