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Simplifying 2x2 + 10x + -256 = 0 Reorder the terms: -256 + 10x + 2x2 = 0 Solving -256 + 10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-128 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-128 + 5x + x2)' equal to zero and attempt to solve: Simplifying -128 + 5x + x2 = 0 Solving -128 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 5x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 5x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 5x + x2 = 0 + 128 5x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 5x + x2 = 128 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 128 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 128 + 6.25 Combine like terms: 128 + 6.25 = 134.25 6.25 + 5x + x2 = 134.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 2.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 2.5 = 11.586630226 Simplifying x + 2.5 = 11.586630226 Reorder the terms: 2.5 + x = 11.586630226 Solving 2.5 + x = 11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 11.586630226 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.586630226 + -2.5 x = 11.586630226 + -2.5 Combine like terms: 11.586630226 + -2.5 = 9.086630226 x = 9.086630226 Simplifying x = 9.086630226Subproblem 2
x + 2.5 = -11.586630226 Simplifying x + 2.5 = -11.586630226 Reorder the terms: 2.5 + x = -11.586630226 Solving 2.5 + x = -11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -11.586630226 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.586630226 + -2.5 x = -11.586630226 + -2.5 Combine like terms: -11.586630226 + -2.5 = -14.086630226 x = -14.086630226 Simplifying x = -14.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.086630226, -14.086630226}Solution
x = {9.086630226, -14.086630226}
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