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Simplifying 2x2 + -26x + -128 = 0 Reorder the terms: -128 + -26x + 2x2 = 0 Solving -128 + -26x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + -13x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-64 + -13x + x2)' equal to zero and attempt to solve: Simplifying -64 + -13x + x2 = 0 Solving -64 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -13x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -13x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -13x + x2 = 0 + 64 -13x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -13x + x2 = 64 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 64 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 64 + 42.25 Combine like terms: 64 + 42.25 = 106.25 42.25 + -13x + x2 = 106.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -6.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -6.5 = 10.307764064 Simplifying x + -6.5 = 10.307764064 Reorder the terms: -6.5 + x = 10.307764064 Solving -6.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 10.307764064 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 10.307764064 + 6.5 x = 10.307764064 + 6.5 Combine like terms: 10.307764064 + 6.5 = 16.807764064 x = 16.807764064 Simplifying x = 16.807764064Subproblem 2
x + -6.5 = -10.307764064 Simplifying x + -6.5 = -10.307764064 Reorder the terms: -6.5 + x = -10.307764064 Solving -6.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -10.307764064 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -10.307764064 + 6.5 x = -10.307764064 + 6.5 Combine like terms: -10.307764064 + 6.5 = -3.807764064 x = -3.807764064 Simplifying x = -3.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.807764064, -3.807764064}Solution
x = {16.807764064, -3.807764064}
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