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Simplifying 2x2 + 22x + -13 = 0 Reorder the terms: -13 + 22x + 2x2 = 0 Solving -13 + 22x + 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'. -6.5 + 11x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 11x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 11x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 11x + x2 = 0 + 6.5 11x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 11x + x2 = 6.5 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 6.5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 6.5 + 30.25 Combine like terms: 6.5 + 30.25 = 36.75 30.25 + 11x + x2 = 36.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + 5.5) equal to 6.062177826 and -6.062177826.Subproblem 1
x + 5.5 = 6.062177826 Simplifying x + 5.5 = 6.062177826 Reorder the terms: 5.5 + x = 6.062177826 Solving 5.5 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.062177826 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.062177826 + -5.5 x = 6.062177826 + -5.5 Combine like terms: 6.062177826 + -5.5 = 0.562177826 x = 0.562177826 Simplifying x = 0.562177826Subproblem 2
x + 5.5 = -6.062177826 Simplifying x + 5.5 = -6.062177826 Reorder the terms: 5.5 + x = -6.062177826 Solving 5.5 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.062177826 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.062177826 + -5.5 x = -6.062177826 + -5.5 Combine like terms: -6.062177826 + -5.5 = -11.562177826 x = -11.562177826 Simplifying x = -11.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.562177826, -11.562177826}
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