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Simplifying 0 = -16x2 + 64x + 8 Reorder the terms: 0 = 8 + 64x + -16x2 Solving 0 = 8 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -64x + 16x2 = 8 + 64x + -16x2 + -8 + -64x + 16x2 Reorder the terms: -8 + -64x + 16x2 = 8 + -8 + 64x + -64x + -16x2 + 16x2 Combine like terms: 8 + -8 = 0 -8 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -8 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -8 + -64x + 16x2 = 0 + -16x2 + 16x2 -8 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -8 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-1 + -8x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -8x + 2x2 = 0 Solving -1 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -4x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4x + x2 = 0 + 0.5 -4x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4x + x2 = 0.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.5 + 4 Reorder the terms: 4 + -4x + x2 = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 4 + -4x + x2 = 4.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -2) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -2 = 2.121320344 Simplifying x + -2 = 2.121320344 Reorder the terms: -2 + x = 2.121320344 Solving -2 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.121320344 + 2 x = 2.121320344 + 2 Combine like terms: 2.121320344 + 2 = 4.121320344 x = 4.121320344 Simplifying x = 4.121320344Subproblem 2
x + -2 = -2.121320344 Simplifying x + -2 = -2.121320344 Reorder the terms: -2 + x = -2.121320344 Solving -2 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.121320344 + 2 x = -2.121320344 + 2 Combine like terms: -2.121320344 + 2 = -0.121320344 x = -0.121320344 Simplifying x = -0.121320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.121320344, -0.121320344}Solution
x = {4.121320344, -0.121320344}
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