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Simplifying -16x2 + 250x + 300 = 0 Reorder the terms: 300 + 250x + -16x2 = 0 Solving 300 + 250x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(150 + 125x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(150 + 125x + -8x2)' equal to zero and attempt to solve: Simplifying 150 + 125x + -8x2 = 0 Solving 150 + 125x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -18.75 + -15.625x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -15.625x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -15.625x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -15.625x + x2 = 0 + 18.75 -15.625x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -15.625x + x2 = 18.75 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 = 18.75 + 61.03515625 Reorder the terms: 61.03515625 + -15.625x + x2 = 18.75 + 61.03515625 Combine like terms: 18.75 + 61.03515625 = 79.78515625 61.03515625 + -15.625x + x2 = 79.78515625 Factor a perfect square on the left side: (x + -7.8125)(x + -7.8125) = 79.78515625 Calculate the square root of the right side: 8.932253705 Break this problem into two subproblems by setting (x + -7.8125) equal to 8.932253705 and -8.932253705.Subproblem 1
x + -7.8125 = 8.932253705 Simplifying x + -7.8125 = 8.932253705 Reorder the terms: -7.8125 + x = 8.932253705 Solving -7.8125 + x = 8.932253705 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 = 8.932253705 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + x = 8.932253705 + 7.8125 x = 8.932253705 + 7.8125 Combine like terms: 8.932253705 + 7.8125 = 16.744753705 x = 16.744753705 Simplifying x = 16.744753705Subproblem 2
x + -7.8125 = -8.932253705 Simplifying x + -7.8125 = -8.932253705 Reorder the terms: -7.8125 + x = -8.932253705 Solving -7.8125 + x = -8.932253705 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 = -8.932253705 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + x = -8.932253705 + 7.8125 x = -8.932253705 + 7.8125 Combine like terms: -8.932253705 + 7.8125 = -1.119753705 x = -1.119753705 Simplifying x = -1.119753705Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.744753705, -1.119753705}Solution
x = {16.744753705, -1.119753705}
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