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Simplifying 4x2 + -80x + -200 = 1250 Reorder the terms: -200 + -80x + 4x2 = 1250 Solving -200 + -80x + 4x2 = 1250 Solving for variable 'x'. Reorder the terms: -200 + -1250 + -80x + 4x2 = 1250 + -1250 Combine like terms: -200 + -1250 = -1450 -1450 + -80x + 4x2 = 1250 + -1250 Combine like terms: 1250 + -1250 = 0 -1450 + -80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-725 + -40x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-725 + -40x + 2x2)' equal to zero and attempt to solve: Simplifying -725 + -40x + 2x2 = 0 Solving -725 + -40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -362.5 + -20x + x2 = 0 Move the constant term to the right: Add '362.5' to each side of the equation. -362.5 + -20x + 362.5 + x2 = 0 + 362.5 Reorder the terms: -362.5 + 362.5 + -20x + x2 = 0 + 362.5 Combine like terms: -362.5 + 362.5 = 0.0 0.0 + -20x + x2 = 0 + 362.5 -20x + x2 = 0 + 362.5 Combine like terms: 0 + 362.5 = 362.5 -20x + x2 = 362.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 362.5 + 100 Reorder the terms: 100 + -20x + x2 = 362.5 + 100 Combine like terms: 362.5 + 100 = 462.5 100 + -20x + x2 = 462.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 462.5 Calculate the square root of the right side: 21.505813168 Break this problem into two subproblems by setting (x + -10) equal to 21.505813168 and -21.505813168.Subproblem 1
x + -10 = 21.505813168 Simplifying x + -10 = 21.505813168 Reorder the terms: -10 + x = 21.505813168 Solving -10 + x = 21.505813168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 21.505813168 + 10 Combine like terms: -10 + 10 = 0 0 + x = 21.505813168 + 10 x = 21.505813168 + 10 Combine like terms: 21.505813168 + 10 = 31.505813168 x = 31.505813168 Simplifying x = 31.505813168Subproblem 2
x + -10 = -21.505813168 Simplifying x + -10 = -21.505813168 Reorder the terms: -10 + x = -21.505813168 Solving -10 + x = -21.505813168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -21.505813168 + 10 Combine like terms: -10 + 10 = 0 0 + x = -21.505813168 + 10 x = -21.505813168 + 10 Combine like terms: -21.505813168 + 10 = -11.505813168 x = -11.505813168 Simplifying x = -11.505813168Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.505813168, -11.505813168}Solution
x = {31.505813168, -11.505813168}
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