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Simplifying 0 = -4x2 + 100x + -500 Reorder the terms: 0 = -500 + 100x + -4x2 Solving 0 = -500 + 100x + -4x2 Solving for variable 'x'. Combine like terms: 0 + 500 = 500 500 + -100x + 4x2 = -500 + 100x + -4x2 + 500 + -100x + 4x2 Reorder the terms: 500 + -100x + 4x2 = -500 + 500 + 100x + -100x + -4x2 + 4x2 Combine like terms: -500 + 500 = 0 500 + -100x + 4x2 = 0 + 100x + -100x + -4x2 + 4x2 500 + -100x + 4x2 = 100x + -100x + -4x2 + 4x2 Combine like terms: 100x + -100x = 0 500 + -100x + 4x2 = 0 + -4x2 + 4x2 500 + -100x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 500 + -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(125 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(125 + -25x + x2)' equal to zero and attempt to solve: Simplifying 125 + -25x + x2 = 0 Solving 125 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -25x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + -25x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -25x + x2 = 0 + -125 -25x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 -25x + x2 = -125 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -125 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -125 + 156.25 Combine like terms: -125 + 156.25 = 31.25 156.25 + -25x + x2 = 31.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -12.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -12.5 = 5.590169944 Simplifying x + -12.5 = 5.590169944 Reorder the terms: -12.5 + x = 5.590169944 Solving -12.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 5.590169944 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 5.590169944 + 12.5 x = 5.590169944 + 12.5 Combine like terms: 5.590169944 + 12.5 = 18.090169944 x = 18.090169944 Simplifying x = 18.090169944Subproblem 2
x + -12.5 = -5.590169944 Simplifying x + -12.5 = -5.590169944 Reorder the terms: -12.5 + x = -5.590169944 Solving -12.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -5.590169944 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -5.590169944 + 12.5 x = -5.590169944 + 12.5 Combine like terms: -5.590169944 + 12.5 = 6.909830056 x = 6.909830056 Simplifying x = 6.909830056Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.090169944, 6.909830056}Solution
x = {18.090169944, 6.909830056}
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