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Simplifying 2x2 + -49x + 26 = 0 Reorder the terms: 26 + -49x + 2x2 = 0 Solving 26 + -49x + 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'. 13 + -24.5x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -24.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -24.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -24.5x + x2 = 0 + -13 -24.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -24.5x + x2 = -13 The x term is -24.5x. Take half its coefficient (-12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. -24.5x + 150.0625 + x2 = -13 + 150.0625 Reorder the terms: 150.0625 + -24.5x + x2 = -13 + 150.0625 Combine like terms: -13 + 150.0625 = 137.0625 150.0625 + -24.5x + x2 = 137.0625 Factor a perfect square on the left side: (x + -12.25)(x + -12.25) = 137.0625 Calculate the square root of the right side: 11.707369474 Break this problem into two subproblems by setting (x + -12.25) equal to 11.707369474 and -11.707369474.Subproblem 1
x + -12.25 = 11.707369474 Simplifying x + -12.25 = 11.707369474 Reorder the terms: -12.25 + x = 11.707369474 Solving -12.25 + x = 11.707369474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = 11.707369474 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = 11.707369474 + 12.25 x = 11.707369474 + 12.25 Combine like terms: 11.707369474 + 12.25 = 23.957369474 x = 23.957369474 Simplifying x = 23.957369474Subproblem 2
x + -12.25 = -11.707369474 Simplifying x + -12.25 = -11.707369474 Reorder the terms: -12.25 + x = -11.707369474 Solving -12.25 + x = -11.707369474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = -11.707369474 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = -11.707369474 + 12.25 x = -11.707369474 + 12.25 Combine like terms: -11.707369474 + 12.25 = 0.542630526 x = 0.542630526 Simplifying x = 0.542630526Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.957369474, 0.542630526}
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