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Simplifying x = -16x2 + 32x + 64 Reorder the terms: x = 64 + 32x + -16x2 Solving x = 64 + 32x + -16x2 Solving for variable 'x'. Reorder the terms: -64 + x + -32x + 16x2 = 64 + 32x + -16x2 + -64 + -32x + 16x2 Combine like terms: x + -32x = -31x -64 + -31x + 16x2 = 64 + 32x + -16x2 + -64 + -32x + 16x2 Reorder the terms: -64 + -31x + 16x2 = 64 + -64 + 32x + -32x + -16x2 + 16x2 Combine like terms: 64 + -64 = 0 -64 + -31x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -64 + -31x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -64 + -31x + 16x2 = 0 + -16x2 + 16x2 -64 + -31x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -64 + -31x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4 + -1.9375x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.9375x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.9375x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.9375x + x2 = 0 + 4 -1.9375x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.9375x + x2 = 4 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 = 4 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = 4 + 0.9384765625 Combine like terms: 4 + 0.9384765625 = 4.9384765625 0.9384765625 + -1.9375x + x2 = 4.9384765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 4.9384765625 Calculate the square root of the right side: 2.222268337 Break this problem into two subproblems by setting (x + -0.96875) equal to 2.222268337 and -2.222268337.Subproblem 1
x + -0.96875 = 2.222268337 Simplifying x + -0.96875 = 2.222268337 Reorder the terms: -0.96875 + x = 2.222268337 Solving -0.96875 + x = 2.222268337 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 = 2.222268337 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 2.222268337 + 0.96875 x = 2.222268337 + 0.96875 Combine like terms: 2.222268337 + 0.96875 = 3.191018337 x = 3.191018337 Simplifying x = 3.191018337Subproblem 2
x + -0.96875 = -2.222268337 Simplifying x + -0.96875 = -2.222268337 Reorder the terms: -0.96875 + x = -2.222268337 Solving -0.96875 + x = -2.222268337 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 = -2.222268337 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -2.222268337 + 0.96875 x = -2.222268337 + 0.96875 Combine like terms: -2.222268337 + 0.96875 = -1.253518337 x = -1.253518337 Simplifying x = -1.253518337Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.191018337, -1.253518337}
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