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Simplifying 4x2 + -64x + 8 = 0 Reorder the terms: 8 + -64x + 4x2 = 0 Solving 8 + -64x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -16x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -16x + x2)' equal to zero and attempt to solve: Simplifying 2 + -16x + x2 = 0 Solving 2 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -16x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -16x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -16x + x2 = 0 + -2 -16x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -16x + x2 = -2 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 = -2 + 64 Reorder the terms: 64 + -16x + x2 = -2 + 64 Combine like terms: -2 + 64 = 62 64 + -16x + x2 = 62 Factor a perfect square on the left side: (x + -8)(x + -8) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -8) equal to 7.874007874 and -7.874007874.Subproblem 1
x + -8 = 7.874007874 Simplifying x + -8 = 7.874007874 Reorder the terms: -8 + x = 7.874007874 Solving -8 + x = 7.874007874 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 = 7.874007874 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.874007874 + 8 x = 7.874007874 + 8 Combine like terms: 7.874007874 + 8 = 15.874007874 x = 15.874007874 Simplifying x = 15.874007874Subproblem 2
x + -8 = -7.874007874 Simplifying x + -8 = -7.874007874 Reorder the terms: -8 + x = -7.874007874 Solving -8 + x = -7.874007874 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 = -7.874007874 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.874007874 + 8 x = -7.874007874 + 8 Combine like terms: -7.874007874 + 8 = 0.125992126 x = 0.125992126 Simplifying x = 0.125992126Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.874007874, 0.125992126}Solution
x = {15.874007874, 0.125992126}
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