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Simplifying 8x2 + -64x + -16 = 0 Reorder the terms: -16 + -64x + 8x2 = 0 Solving -16 + -64x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + -8x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -8x + x2)' equal to zero and attempt to solve: Simplifying -2 + -8x + x2 = 0 Solving -2 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -8x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -8x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8x + x2 = 0 + 2 -8x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8x + x2 = 2 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 = 2 + 16 Reorder the terms: 16 + -8x + x2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + -8x + x2 = 18 Factor a perfect square on the left side: (x + -4)(x + -4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -4) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -4 = 4.242640687 Simplifying x + -4 = 4.242640687 Reorder the terms: -4 + x = 4.242640687 Solving -4 + x = 4.242640687 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 = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.242640687 + 4 x = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 x = 8.242640687 Simplifying x = 8.242640687Subproblem 2
x + -4 = -4.242640687 Simplifying x + -4 = -4.242640687 Reorder the terms: -4 + x = -4.242640687 Solving -4 + x = -4.242640687 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 = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.242640687 + 4 x = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 x = -0.242640687 Simplifying x = -0.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.242640687, -0.242640687}Solution
x = {8.242640687, -0.242640687}
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