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Simplifying 16x2 + 31x + 2 = 0 Reorder the terms: 2 + 31x + 16x2 = 0 Solving 2 + 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'. 0.125 + 1.9375x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 1.9375x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 1.9375x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 1.9375x + x2 = 0 + -0.125 1.9375x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 1.9375x + x2 = -0.125 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 = -0.125 + 0.9384765625 Reorder the terms: 0.9384765625 + 1.9375x + x2 = -0.125 + 0.9384765625 Combine like terms: -0.125 + 0.9384765625 = 0.8134765625 0.9384765625 + 1.9375x + x2 = 0.8134765625 Factor a perfect square on the left side: (x + 0.96875)(x + 0.96875) = 0.8134765625 Calculate the square root of the right side: 0.901929356 Break this problem into two subproblems by setting (x + 0.96875) equal to 0.901929356 and -0.901929356.Subproblem 1
x + 0.96875 = 0.901929356 Simplifying x + 0.96875 = 0.901929356 Reorder the terms: 0.96875 + x = 0.901929356 Solving 0.96875 + x = 0.901929356 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 = 0.901929356 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = 0.901929356 + -0.96875 x = 0.901929356 + -0.96875 Combine like terms: 0.901929356 + -0.96875 = -0.066820644 x = -0.066820644 Simplifying x = -0.066820644Subproblem 2
x + 0.96875 = -0.901929356 Simplifying x + 0.96875 = -0.901929356 Reorder the terms: 0.96875 + x = -0.901929356 Solving 0.96875 + x = -0.901929356 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 = -0.901929356 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = -0.901929356 + -0.96875 x = -0.901929356 + -0.96875 Combine like terms: -0.901929356 + -0.96875 = -1.870679356 x = -1.870679356 Simplifying x = -1.870679356Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.066820644, -1.870679356}
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