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Simplifying (-16x2) + x + 950 = 0 Reorder the terms: 950 + x + (-16x2) = 0 Solving 950 + x + (-16x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -59.375 + -0.0625x + x2 = 0 Move the constant term to the right: Add '59.375' to each side of the equation. -59.375 + -0.0625x + 59.375 + x2 = 0 + 59.375 Reorder the terms: -59.375 + 59.375 + -0.0625x + x2 = 0 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + -0.0625x + x2 = 0 + 59.375 -0.0625x + x2 = 0 + 59.375 Combine like terms: 0 + 59.375 = 59.375 -0.0625x + x2 = 59.375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.0625x + 0.25 + x2 = 59.375 + 0.25 Reorder the terms: 0.25 + -0.0625x + x2 = 59.375 + 0.25 Combine like terms: 59.375 + 0.25 = 59.625 0.25 + -0.0625x + x2 = 59.625 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 59.625 Calculate the square root of the right side: 7.721722606 Break this problem into two subproblems by setting ((x) + 0.5) equal to 7.721722606 and -7.721722606.Subproblem 1
(x) + 0.5 = 7.721722606 Simplifying (x) + 0.5 = 7.721722606 x + 0.5 = 7.721722606 Reorder the terms: 0.5 + x = 7.721722606 Solving 0.5 + x = 7.721722606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.721722606 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.721722606 + -0.5 x = 7.721722606 + -0.5 Combine like terms: 7.721722606 + -0.5 = 7.221722606 x = 7.221722606 Simplifying x = 7.221722606Subproblem 2
(x) + 0.5 = -7.721722606 Simplifying (x) + 0.5 = -7.721722606 x + 0.5 = -7.721722606 Reorder the terms: 0.5 + x = -7.721722606 Solving 0.5 + x = -7.721722606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.721722606 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.721722606 + -0.5 x = -7.721722606 + -0.5 Combine like terms: -7.721722606 + -0.5 = -8.221722606 x = -8.221722606 Simplifying x = -8.221722606Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.221722606, -8.221722606}
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