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Simplifying 2x2 + -26x + -25 = 0 Reorder the terms: -25 + -26x + 2x2 = 0 Solving -25 + -26x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -13x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -13x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -13x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -13x + x2 = 0 + 12.5 -13x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -13x + x2 = 12.5 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 = 12.5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 12.5 + 42.25 Combine like terms: 12.5 + 42.25 = 54.75 42.25 + -13x + x2 = 54.75 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 54.75 Calculate the square root of the right side: 7.399324293 Break this problem into two subproblems by setting (x + -6.5) equal to 7.399324293 and -7.399324293.Subproblem 1
x + -6.5 = 7.399324293 Simplifying x + -6.5 = 7.399324293 Reorder the terms: -6.5 + x = 7.399324293 Solving -6.5 + x = 7.399324293 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 = 7.399324293 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.399324293 + 6.5 x = 7.399324293 + 6.5 Combine like terms: 7.399324293 + 6.5 = 13.899324293 x = 13.899324293 Simplifying x = 13.899324293Subproblem 2
x + -6.5 = -7.399324293 Simplifying x + -6.5 = -7.399324293 Reorder the terms: -6.5 + x = -7.399324293 Solving -6.5 + x = -7.399324293 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 = -7.399324293 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.399324293 + 6.5 x = -7.399324293 + 6.5 Combine like terms: -7.399324293 + 6.5 = -0.899324293 x = -0.899324293 Simplifying x = -0.899324293Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.899324293, -0.899324293}
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