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Simplifying 2x2 + -4x + -128 = 0 Reorder the terms: -128 + -4x + 2x2 = 0 Solving -128 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-64 + -2x + x2)' equal to zero and attempt to solve: Simplifying -64 + -2x + x2 = 0 Solving -64 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -2x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -2x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -2x + x2 = 0 + 64 -2x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -2x + x2 = 64 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 = 64 + 1 Reorder the terms: 1 + -2x + x2 = 64 + 1 Combine like terms: 64 + 1 = 65 1 + -2x + x2 = 65 Factor a perfect square on the left side: (x + -1)(x + -1) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -1) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -1 = 8.062257748 Simplifying x + -1 = 8.062257748 Reorder the terms: -1 + x = 8.062257748 Solving -1 + x = 8.062257748 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 = 8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.062257748 + 1 x = 8.062257748 + 1 Combine like terms: 8.062257748 + 1 = 9.062257748 x = 9.062257748 Simplifying x = 9.062257748Subproblem 2
x + -1 = -8.062257748 Simplifying x + -1 = -8.062257748 Reorder the terms: -1 + x = -8.062257748 Solving -1 + x = -8.062257748 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 = -8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.062257748 + 1 x = -8.062257748 + 1 Combine like terms: -8.062257748 + 1 = -7.062257748 x = -7.062257748 Simplifying x = -7.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.062257748, -7.062257748}Solution
x = {9.062257748, -7.062257748}
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