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Simplifying 8x2 + -2x + -256 = 0 Reorder the terms: -256 + -2x + 8x2 = 0 Solving -256 + -2x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-128 + -1x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-128 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying -128 + -1x + 4x2 = 0 Solving -128 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -32 + -0.25x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.25x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -0.25x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.25x + x2 = 0 + 32 -0.25x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.25x + x2 = 32 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 32 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 32 + 0.015625 Combine like terms: 32 + 0.015625 = 32.015625 0.015625 + -0.25x + x2 = 32.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 32.015625 Calculate the square root of the right side: 5.658235149 Break this problem into two subproblems by setting (x + -0.125) equal to 5.658235149 and -5.658235149.Subproblem 1
x + -0.125 = 5.658235149 Simplifying x + -0.125 = 5.658235149 Reorder the terms: -0.125 + x = 5.658235149 Solving -0.125 + x = 5.658235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 5.658235149 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 5.658235149 + 0.125 x = 5.658235149 + 0.125 Combine like terms: 5.658235149 + 0.125 = 5.783235149 x = 5.783235149 Simplifying x = 5.783235149Subproblem 2
x + -0.125 = -5.658235149 Simplifying x + -0.125 = -5.658235149 Reorder the terms: -0.125 + x = -5.658235149 Solving -0.125 + x = -5.658235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -5.658235149 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -5.658235149 + 0.125 x = -5.658235149 + 0.125 Combine like terms: -5.658235149 + 0.125 = -5.533235149 x = -5.533235149 Simplifying x = -5.533235149Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.783235149, -5.533235149}Solution
x = {5.783235149, -5.533235149}
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