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Simplifying -8x2 + 125x + -305 = 0 Reorder the terms: -305 + 125x + -8x2 = 0 Solving -305 + 125x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 38.125 + -15.625x + x2 = 0 Move the constant term to the right: Add '-38.125' to each side of the equation. 38.125 + -15.625x + -38.125 + x2 = 0 + -38.125 Reorder the terms: 38.125 + -38.125 + -15.625x + x2 = 0 + -38.125 Combine like terms: 38.125 + -38.125 = 0.000 0.000 + -15.625x + x2 = 0 + -38.125 -15.625x + x2 = 0 + -38.125 Combine like terms: 0 + -38.125 = -38.125 -15.625x + x2 = -38.125 The x term is -15.625x. Take half its coefficient (-7.8125). Square it (61.03515625) and add it to both sides. Add '61.03515625' to each side of the equation. -15.625x + 61.03515625 + x2 = -38.125 + 61.03515625 Reorder the terms: 61.03515625 + -15.625x + x2 = -38.125 + 61.03515625 Combine like terms: -38.125 + 61.03515625 = 22.91015625 61.03515625 + -15.625x + x2 = 22.91015625 Factor a perfect square on the left side: (x + -7.8125)(x + -7.8125) = 22.91015625 Calculate the square root of the right side: 4.7864555 Break this problem into two subproblems by setting (x + -7.8125) equal to 4.7864555 and -4.7864555.Subproblem 1
x + -7.8125 = 4.7864555 Simplifying x + -7.8125 = 4.7864555 Reorder the terms: -7.8125 + x = 4.7864555 Solving -7.8125 + x = 4.7864555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.8125' to each side of the equation. -7.8125 + 7.8125 + x = 4.7864555 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + x = 4.7864555 + 7.8125 x = 4.7864555 + 7.8125 Combine like terms: 4.7864555 + 7.8125 = 12.5989555 x = 12.5989555 Simplifying x = 12.5989555Subproblem 2
x + -7.8125 = -4.7864555 Simplifying x + -7.8125 = -4.7864555 Reorder the terms: -7.8125 + x = -4.7864555 Solving -7.8125 + x = -4.7864555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.8125' to each side of the equation. -7.8125 + 7.8125 + x = -4.7864555 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + x = -4.7864555 + 7.8125 x = -4.7864555 + 7.8125 Combine like terms: -4.7864555 + 7.8125 = 3.0260445 x = 3.0260445 Simplifying x = 3.0260445Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5989555, 3.0260445}
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