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Simplifying 2x2 + -32x + 64 = 0 Reorder the terms: 64 + -32x + 2x2 = 0 Solving 64 + -32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -16x + x2)' equal to zero and attempt to solve: Simplifying 32 + -16x + x2 = 0 Solving 32 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -16x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -16x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -16x + x2 = 0 + -32 -16x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -16x + x2 = -32 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -32 + 64 Reorder the terms: 64 + -16x + x2 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + -16x + x2 = 32 Factor a perfect square on the left side: (x + -8)(x + -8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -8) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -8 = 5.656854249 Simplifying x + -8 = 5.656854249 Reorder the terms: -8 + x = 5.656854249 Solving -8 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x = 5.656854249 + 8 x = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 x = 13.656854249 Simplifying x = 13.656854249Subproblem 2
x + -8 = -5.656854249 Simplifying x + -8 = -5.656854249 Reorder the terms: -8 + x = -5.656854249 Solving -8 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x = -5.656854249 + 8 x = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 x = 2.343145751 Simplifying x = 2.343145751Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.656854249, 2.343145751}Solution
x = {13.656854249, 2.343145751}
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