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Simplifying 8x2 + 80x + -500 = 0 Reorder the terms: -500 + 80x + 8x2 = 0 Solving -500 + 80x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-125 + 20x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-125 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying -125 + 20x + 2x2 = 0 Solving -125 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + 10x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + 10x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + 10x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + 10x + x2 = 0 + 62.5 10x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 10x + x2 = 62.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 62.5 + 25 Reorder the terms: 25 + 10x + x2 = 62.5 + 25 Combine like terms: 62.5 + 25 = 87.5 25 + 10x + x2 = 87.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 87.5 Calculate the square root of the right side: 9.354143467 Break this problem into two subproblems by setting (x + 5) equal to 9.354143467 and -9.354143467.Subproblem 1
x + 5 = 9.354143467 Simplifying x + 5 = 9.354143467 Reorder the terms: 5 + x = 9.354143467 Solving 5 + x = 9.354143467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.354143467 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.354143467 + -5 x = 9.354143467 + -5 Combine like terms: 9.354143467 + -5 = 4.354143467 x = 4.354143467 Simplifying x = 4.354143467Subproblem 2
x + 5 = -9.354143467 Simplifying x + 5 = -9.354143467 Reorder the terms: 5 + x = -9.354143467 Solving 5 + x = -9.354143467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.354143467 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.354143467 + -5 x = -9.354143467 + -5 Combine like terms: -9.354143467 + -5 = -14.354143467 x = -14.354143467 Simplifying x = -14.354143467Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.354143467, -14.354143467}Solution
x = {4.354143467, -14.354143467}
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