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Simplifying x = 14 + 32x + -16x2 Solving x = 14 + 32x + -16x2 Solving for variable 'x'. Reorder the terms: -14 + x + -32x + 16x2 = 14 + 32x + -16x2 + -14 + -32x + 16x2 Combine like terms: x + -32x = -31x -14 + -31x + 16x2 = 14 + 32x + -16x2 + -14 + -32x + 16x2 Reorder the terms: -14 + -31x + 16x2 = 14 + -14 + 32x + -32x + -16x2 + 16x2 Combine like terms: 14 + -14 = 0 -14 + -31x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -14 + -31x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -14 + -31x + 16x2 = 0 + -16x2 + 16x2 -14 + -31x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 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 = 2.315403839 x = 2.315403839 Simplifying x = 2.315403839Subproblem 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 = -0.377903839 x = -0.377903839 Simplifying x = -0.377903839Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.315403839, -0.377903839}
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