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Simplifying 16x2 + -31x + 14 = 0 Reorder the terms: 14 + -31x + 16x2 = 0 Solving 14 + -31x + 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'. 0.875 + -1.9375x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -1.9375x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -1.9375x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -1.9375x + x2 = 0 + -0.875 -1.9375x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -1.9375x + x2 = -0.875 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 = -0.875 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = -0.875 + 0.9384765625 Combine like terms: -0.875 + 0.9384765625 = 0.0634765625 0.9384765625 + -1.9375x + x2 = 0.0634765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 0.0634765625 Calculate the square root of the right side: 0.251945555 Break this problem into two subproblems by setting (x + -0.96875) equal to 0.251945555 and -0.251945555.Subproblem 1
x + -0.96875 = 0.251945555 Simplifying x + -0.96875 = 0.251945555 Reorder the terms: -0.96875 + x = 0.251945555 Solving -0.96875 + x = 0.251945555 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 = 0.251945555 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 0.251945555 + 0.96875 x = 0.251945555 + 0.96875 Combine like terms: 0.251945555 + 0.96875 = 1.220695555 x = 1.220695555 Simplifying x = 1.220695555Subproblem 2
x + -0.96875 = -0.251945555 Simplifying x + -0.96875 = -0.251945555 Reorder the terms: -0.96875 + x = -0.251945555 Solving -0.96875 + x = -0.251945555 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 = -0.251945555 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -0.251945555 + 0.96875 x = -0.251945555 + 0.96875 Combine like terms: -0.251945555 + 0.96875 = 0.716804445 x = 0.716804445 Simplifying x = 0.716804445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.220695555, 0.716804445}
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