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Simplifying 0 = -16x2 + 64x + 32 Reorder the terms: 0 = 32 + 64x + -16x2 Solving 0 = 32 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -64x + 16x2 = 32 + 64x + -16x2 + -32 + -64x + 16x2 Reorder the terms: -32 + -64x + 16x2 = 32 + -32 + 64x + -64x + -16x2 + 16x2 Combine like terms: 32 + -32 = 0 -32 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -32 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -32 + -64x + 16x2 = 0 + -16x2 + 16x2 -32 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -32 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-2 + -4x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -4x + x2)' equal to zero and attempt to solve: Simplifying -2 + -4x + x2 = 0 Solving -2 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4x + x2 = 0 + 2 -4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4x + x2 = 2 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 = 2 + 4 Reorder the terms: 4 + -4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4x + x2 = 6 Factor a perfect square on the left side: (x + -2)(x + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -2 = 2.449489743 Simplifying x + -2 = 2.449489743 Reorder the terms: -2 + x = 2.449489743 Solving -2 + x = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.449489743 + 2 x = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 x = 4.449489743 Simplifying x = 4.449489743Subproblem 2
x + -2 = -2.449489743 Simplifying x + -2 = -2.449489743 Reorder the terms: -2 + x = -2.449489743 Solving -2 + x = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.449489743 + 2 x = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 x = -0.449489743 Simplifying x = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.449489743, -0.449489743}Solution
x = {4.449489743, -0.449489743}
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