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Simplifying 2x2 + -26x = 23 Reorder the terms: -26x + 2x2 = 23 Solving -26x + 2x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -26x + 2x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -26x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -13x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -13x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -13x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -13x + x2 = 0 + 11.5 -13x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -13x + x2 = 11.5 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 = 11.5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 11.5 + 42.25 Combine like terms: 11.5 + 42.25 = 53.75 42.25 + -13x + x2 = 53.75 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 53.75 Calculate the square root of the right side: 7.331439149 Break this problem into two subproblems by setting (x + -6.5) equal to 7.331439149 and -7.331439149.Subproblem 1
x + -6.5 = 7.331439149 Simplifying x + -6.5 = 7.331439149 Reorder the terms: -6.5 + x = 7.331439149 Solving -6.5 + x = 7.331439149 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 = 7.331439149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.331439149 + 6.5 x = 7.331439149 + 6.5 Combine like terms: 7.331439149 + 6.5 = 13.831439149 x = 13.831439149 Simplifying x = 13.831439149Subproblem 2
x + -6.5 = -7.331439149 Simplifying x + -6.5 = -7.331439149 Reorder the terms: -6.5 + x = -7.331439149 Solving -6.5 + x = -7.331439149 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 = -7.331439149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.331439149 + 6.5 x = -7.331439149 + 6.5 Combine like terms: -7.331439149 + 6.5 = -0.831439149 x = -0.831439149 Simplifying x = -0.831439149Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.831439149, -0.831439149}
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