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Simplifying x2 + x2 + -16x + 64 = 256 Reorder the terms: 64 + -16x + x2 + x2 = 256 Combine like terms: x2 + x2 = 2x2 64 + -16x + 2x2 = 256 Solving 64 + -16x + 2x2 = 256 Solving for variable 'x'. Reorder the terms: 64 + -256 + -16x + 2x2 = 256 + -256 Combine like terms: 64 + -256 = -192 -192 + -16x + 2x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -192 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-96 + -8x + x2)' equal to zero and attempt to solve: Simplifying -96 + -8x + x2 = 0 Solving -96 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -8x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -8x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -8x + x2 = 0 + 96 -8x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -8x + x2 = 96 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 96 + 16 Reorder the terms: 16 + -8x + x2 = 96 + 16 Combine like terms: 96 + 16 = 112 16 + -8x + x2 = 112 Factor a perfect square on the left side: (x + -4)(x + -4) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + -4) equal to 10.583005244 and -10.583005244.Subproblem 1
x + -4 = 10.583005244 Simplifying x + -4 = 10.583005244 Reorder the terms: -4 + x = 10.583005244 Solving -4 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.583005244 + 4 x = 10.583005244 + 4 Combine like terms: 10.583005244 + 4 = 14.583005244 x = 14.583005244 Simplifying x = 14.583005244Subproblem 2
x + -4 = -10.583005244 Simplifying x + -4 = -10.583005244 Reorder the terms: -4 + x = -10.583005244 Solving -4 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.583005244 + 4 x = -10.583005244 + 4 Combine like terms: -10.583005244 + 4 = -6.583005244 x = -6.583005244 Simplifying x = -6.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.583005244, -6.583005244}Solution
x = {14.583005244, -6.583005244}
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