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Simplifying -1x2 + -25x + -26 = 0 Reorder the terms: -26 + -25x + -1x2 = 0 Solving -26 + -25x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(26 + 25x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(26 + 25x + x2)' equal to zero and attempt to solve: Simplifying 26 + 25x + x2 = 0 Solving 26 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 25x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 25x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 25x + x2 = 0 + -26 25x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 25x + x2 = -26 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -26 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -26 + 156.25 Combine like terms: -26 + 156.25 = 130.25 156.25 + 25x + x2 = 130.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 12.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 12.5 = 11.412712211 Simplifying x + 12.5 = 11.412712211 Reorder the terms: 12.5 + x = 11.412712211 Solving 12.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 11.412712211 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 11.412712211 + -12.5 x = 11.412712211 + -12.5 Combine like terms: 11.412712211 + -12.5 = -1.087287789 x = -1.087287789 Simplifying x = -1.087287789Subproblem 2
x + 12.5 = -11.412712211 Simplifying x + 12.5 = -11.412712211 Reorder the terms: 12.5 + x = -11.412712211 Solving 12.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -11.412712211 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -11.412712211 + -12.5 x = -11.412712211 + -12.5 Combine like terms: -11.412712211 + -12.5 = -23.912712211 x = -23.912712211 Simplifying x = -23.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.087287789, -23.912712211}Solution
x = {-1.087287789, -23.912712211}
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