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Simplifying 2x2 + -4x + -256 = 0 Reorder the terms: -256 + -4x + 2x2 = 0 Solving -256 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-128 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-128 + -2x + x2)' equal to zero and attempt to solve: Simplifying -128 + -2x + x2 = 0 Solving -128 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + -2x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -2x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -2x + x2 = 0 + 128 -2x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -2x + x2 = 128 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 = 128 + 1 Reorder the terms: 1 + -2x + x2 = 128 + 1 Combine like terms: 128 + 1 = 129 1 + -2x + x2 = 129 Factor a perfect square on the left side: (x + -1)(x + -1) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -1) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -1 = 11.357816692 Simplifying x + -1 = 11.357816692 Reorder the terms: -1 + x = 11.357816692 Solving -1 + x = 11.357816692 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 = 11.357816692 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.357816692 + 1 x = 11.357816692 + 1 Combine like terms: 11.357816692 + 1 = 12.357816692 x = 12.357816692 Simplifying x = 12.357816692Subproblem 2
x + -1 = -11.357816692 Simplifying x + -1 = -11.357816692 Reorder the terms: -1 + x = -11.357816692 Solving -1 + x = -11.357816692 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 = -11.357816692 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.357816692 + 1 x = -11.357816692 + 1 Combine like terms: -11.357816692 + 1 = -10.357816692 x = -10.357816692 Simplifying x = -10.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.357816692, -10.357816692}Solution
x = {12.357816692, -10.357816692}
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