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Simplifying -8x2 + -150x + 500 = 0 Reorder the terms: 500 + -150x + -8x2 = 0 Solving 500 + -150x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(250 + -75x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(250 + -75x + -4x2)' equal to zero and attempt to solve: Simplifying 250 + -75x + -4x2 = 0 Solving 250 + -75x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -62.5 + 18.75x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + 18.75x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + 18.75x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + 18.75x + x2 = 0 + 62.5 18.75x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 18.75x + x2 = 62.5 The x term is 18.75x. Take half its coefficient (9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. 18.75x + 87.890625 + x2 = 62.5 + 87.890625 Reorder the terms: 87.890625 + 18.75x + x2 = 62.5 + 87.890625 Combine like terms: 62.5 + 87.890625 = 150.390625 87.890625 + 18.75x + x2 = 150.390625 Factor a perfect square on the left side: (x + 9.375)(x + 9.375) = 150.390625 Calculate the square root of the right side: 12.263385544 Break this problem into two subproblems by setting (x + 9.375) equal to 12.263385544 and -12.263385544.Subproblem 1
x + 9.375 = 12.263385544 Simplifying x + 9.375 = 12.263385544 Reorder the terms: 9.375 + x = 12.263385544 Solving 9.375 + x = 12.263385544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.375' to each side of the equation. 9.375 + -9.375 + x = 12.263385544 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + x = 12.263385544 + -9.375 x = 12.263385544 + -9.375 Combine like terms: 12.263385544 + -9.375 = 2.888385544 x = 2.888385544 Simplifying x = 2.888385544Subproblem 2
x + 9.375 = -12.263385544 Simplifying x + 9.375 = -12.263385544 Reorder the terms: 9.375 + x = -12.263385544 Solving 9.375 + x = -12.263385544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.375' to each side of the equation. 9.375 + -9.375 + x = -12.263385544 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + x = -12.263385544 + -9.375 x = -12.263385544 + -9.375 Combine like terms: -12.263385544 + -9.375 = -21.638385544 x = -21.638385544 Simplifying x = -21.638385544Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.888385544, -21.638385544}Solution
x = {2.888385544, -21.638385544}
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