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Simplifying 16x2 + 31x = 14 Reorder the terms: 31x + 16x2 = 14 Solving 31x + 16x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 31x + 16x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 31x + 16x2 = 0 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 = 1.8134765625 0.9384765625 + 1.9375x + x2 = 1.8134765625 Factor a perfect square on the left side: (x + 0.96875)(x + 0.96875) = 1.8134765625 Calculate the square root of the right side: 1.346653839 Break this problem into two subproblems by setting (x + 0.96875) equal to 1.346653839 and -1.346653839.Subproblem 1
x + 0.96875 = 1.346653839 Simplifying x + 0.96875 = 1.346653839 Reorder the terms: 0.96875 + x = 1.346653839 Solving 0.96875 + x = 1.346653839 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 = 1.346653839 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = 1.346653839 + -0.96875 x = 1.346653839 + -0.96875 Combine like terms: 1.346653839 + -0.96875 = 0.377903839 x = 0.377903839 Simplifying x = 0.377903839Subproblem 2
x + 0.96875 = -1.346653839 Simplifying x + 0.96875 = -1.346653839 Reorder the terms: 0.96875 + x = -1.346653839 Solving 0.96875 + x = -1.346653839 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 = -1.346653839 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = -1.346653839 + -0.96875 x = -1.346653839 + -0.96875 Combine like terms: -1.346653839 + -0.96875 = -2.315403839 x = -2.315403839 Simplifying x = -2.315403839Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.377903839, -2.315403839}
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