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Simplifying 300 = -16x2 + 500x + 10 Reorder the terms: 300 = 10 + 500x + -16x2 Solving 300 = 10 + 500x + -16x2 Solving for variable 'x'. Combine like terms: 300 + -10 = 290 290 + -500x + 16x2 = 10 + 500x + -16x2 + -10 + -500x + 16x2 Reorder the terms: 290 + -500x + 16x2 = 10 + -10 + 500x + -500x + -16x2 + 16x2 Combine like terms: 10 + -10 = 0 290 + -500x + 16x2 = 0 + 500x + -500x + -16x2 + 16x2 290 + -500x + 16x2 = 500x + -500x + -16x2 + 16x2 Combine like terms: 500x + -500x = 0 290 + -500x + 16x2 = 0 + -16x2 + 16x2 290 + -500x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 290 + -500x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(145 + -250x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(145 + -250x + 8x2)' equal to zero and attempt to solve: Simplifying 145 + -250x + 8x2 = 0 Solving 145 + -250x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 18.125 + -31.25x + x2 = 0 Move the constant term to the right: Add '-18.125' to each side of the equation. 18.125 + -31.25x + -18.125 + x2 = 0 + -18.125 Reorder the terms: 18.125 + -18.125 + -31.25x + x2 = 0 + -18.125 Combine like terms: 18.125 + -18.125 = 0.000 0.000 + -31.25x + x2 = 0 + -18.125 -31.25x + x2 = 0 + -18.125 Combine like terms: 0 + -18.125 = -18.125 -31.25x + x2 = -18.125 The x term is -31.25x. Take half its coefficient (-15.625). Square it (244.140625) and add it to both sides. Add '244.140625' to each side of the equation. -31.25x + 244.140625 + x2 = -18.125 + 244.140625 Reorder the terms: 244.140625 + -31.25x + x2 = -18.125 + 244.140625 Combine like terms: -18.125 + 244.140625 = 226.015625 244.140625 + -31.25x + x2 = 226.015625 Factor a perfect square on the left side: (x + -15.625)(x + -15.625) = 226.015625 Calculate the square root of the right side: 15.033816049 Break this problem into two subproblems by setting (x + -15.625) equal to 15.033816049 and -15.033816049.Subproblem 1
x + -15.625 = 15.033816049 Simplifying x + -15.625 = 15.033816049 Reorder the terms: -15.625 + x = 15.033816049 Solving -15.625 + x = 15.033816049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = 15.033816049 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = 15.033816049 + 15.625 x = 15.033816049 + 15.625 Combine like terms: 15.033816049 + 15.625 = 30.658816049 x = 30.658816049 Simplifying x = 30.658816049Subproblem 2
x + -15.625 = -15.033816049 Simplifying x + -15.625 = -15.033816049 Reorder the terms: -15.625 + x = -15.033816049 Solving -15.625 + x = -15.033816049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = -15.033816049 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = -15.033816049 + 15.625 x = -15.033816049 + 15.625 Combine like terms: -15.033816049 + 15.625 = 0.591183951 x = 0.591183951 Simplifying x = 0.591183951Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.658816049, 0.591183951}Solution
x = {30.658816049, 0.591183951}
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