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Simplifying 10 = -16x2 + 31x + 6 Reorder the terms: 10 = 6 + 31x + -16x2 Solving 10 = 6 + 31x + -16x2 Solving for variable 'x'. Combine like terms: 10 + -6 = 4 4 + -31x + 16x2 = 6 + 31x + -16x2 + -6 + -31x + 16x2 Reorder the terms: 4 + -31x + 16x2 = 6 + -6 + 31x + -31x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 4 + -31x + 16x2 = 0 + 31x + -31x + -16x2 + 16x2 4 + -31x + 16x2 = 31x + -31x + -16x2 + 16x2 Combine like terms: 31x + -31x = 0 4 + -31x + 16x2 = 0 + -16x2 + 16x2 4 + -31x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4 + -31x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -1.9375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.9375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.9375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.9375x + x2 = 0 + -0.25 -1.9375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.9375x + x2 = -0.25 The x term is -1.9375x. Take half its coefficient (-0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. -1.9375x + 0.9384765625 + x2 = -0.25 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = -0.25 + 0.9384765625 Combine like terms: -0.25 + 0.9384765625 = 0.6884765625 0.9384765625 + -1.9375x + x2 = 0.6884765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 0.6884765625 Calculate the square root of the right side: 0.829744878 Break this problem into two subproblems by setting (x + -0.96875) equal to 0.829744878 and -0.829744878.Subproblem 1
x + -0.96875 = 0.829744878 Simplifying x + -0.96875 = 0.829744878 Reorder the terms: -0.96875 + x = 0.829744878 Solving -0.96875 + x = 0.829744878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = 0.829744878 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 0.829744878 + 0.96875 x = 0.829744878 + 0.96875 Combine like terms: 0.829744878 + 0.96875 = 1.798494878 x = 1.798494878 Simplifying x = 1.798494878Subproblem 2
x + -0.96875 = -0.829744878 Simplifying x + -0.96875 = -0.829744878 Reorder the terms: -0.96875 + x = -0.829744878 Solving -0.96875 + x = -0.829744878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = -0.829744878 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -0.829744878 + 0.96875 x = -0.829744878 + 0.96875 Combine like terms: -0.829744878 + 0.96875 = 0.139005122 x = 0.139005122 Simplifying x = 0.139005122Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.798494878, 0.139005122}
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