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Simplifying x = 20 + -16x2 + 32x Reorder the terms: x = 20 + 32x + -16x2 Solving x = 20 + 32x + -16x2 Solving for variable 'x'. Reorder the terms: -20 + x + -32x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2 Combine like terms: x + -32x = -31x -20 + -31x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2 Reorder the terms: -20 + -31x + 16x2 = 20 + -20 + 32x + -32x + -16x2 + 16x2 Combine like terms: 20 + -20 = 0 -20 + -31x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -20 + -31x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -20 + -31x + 16x2 = 0 + -16x2 + 16x2 -20 + -31x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -31x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.25 + -1.9375x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.9375x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.9375x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.9375x + x2 = 0 + 1.25 -1.9375x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.9375x + x2 = 1.25 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 = 1.25 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = 1.25 + 0.9384765625 Combine like terms: 1.25 + 0.9384765625 = 2.1884765625 0.9384765625 + -1.9375x + x2 = 2.1884765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 2.1884765625 Calculate the square root of the right side: 1.479350047 Break this problem into two subproblems by setting (x + -0.96875) equal to 1.479350047 and -1.479350047.Subproblem 1
x + -0.96875 = 1.479350047 Simplifying x + -0.96875 = 1.479350047 Reorder the terms: -0.96875 + x = 1.479350047 Solving -0.96875 + x = 1.479350047 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 = 1.479350047 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 1.479350047 + 0.96875 x = 1.479350047 + 0.96875 Combine like terms: 1.479350047 + 0.96875 = 2.448100047 x = 2.448100047 Simplifying x = 2.448100047Subproblem 2
x + -0.96875 = -1.479350047 Simplifying x + -0.96875 = -1.479350047 Reorder the terms: -0.96875 + x = -1.479350047 Solving -0.96875 + x = -1.479350047 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 = -1.479350047 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -1.479350047 + 0.96875 x = -1.479350047 + 0.96875 Combine like terms: -1.479350047 + 0.96875 = -0.510600047 x = -0.510600047 Simplifying x = -0.510600047Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.448100047, -0.510600047}
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