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Simplifying 8x2 + -16x + -128 = 0 Reorder the terms: -128 + -16x + 8x2 = 0 Solving -128 + -16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-16 + -2x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-16 + -2x + x2)' equal to zero and attempt to solve: Simplifying -16 + -2x + x2 = 0 Solving -16 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2x + x2 = 0 + 16 -2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2x + x2 = 16 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 16 + 1 Reorder the terms: 1 + -2x + x2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + -2x + x2 = 17 Factor a perfect square on the left side: (x + -1)(x + -1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -1) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -1 = 4.123105626 Simplifying x + -1 = 4.123105626 Reorder the terms: -1 + x = 4.123105626 Solving -1 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.123105626 + 1 x = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 x = 5.123105626 Simplifying x = 5.123105626Subproblem 2
x + -1 = -4.123105626 Simplifying x + -1 = -4.123105626 Reorder the terms: -1 + x = -4.123105626 Solving -1 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.123105626 + 1 x = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 x = -3.123105626 Simplifying x = -3.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.123105626, -3.123105626}Solution
x = {5.123105626, -3.123105626}
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