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Simplifying 2x2 + 10x + -61 = 0 Reorder the terms: -61 + 10x + 2x2 = 0 Solving -61 + 10x + 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'. -30.5 + 5x + x2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + 5x + 30.5 + x2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + 5x + x2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + 5x + x2 = 0 + 30.5 5x + x2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 5x + x2 = 30.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 30.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 30.5 + 6.25 Combine like terms: 30.5 + 6.25 = 36.75 6.25 + 5x + x2 = 36.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + 2.5) equal to 6.062177826 and -6.062177826.Subproblem 1
x + 2.5 = 6.062177826 Simplifying x + 2.5 = 6.062177826 Reorder the terms: 2.5 + x = 6.062177826 Solving 2.5 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.062177826 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.062177826 + -2.5 x = 6.062177826 + -2.5 Combine like terms: 6.062177826 + -2.5 = 3.562177826 x = 3.562177826 Simplifying x = 3.562177826Subproblem 2
x + 2.5 = -6.062177826 Simplifying x + 2.5 = -6.062177826 Reorder the terms: 2.5 + x = -6.062177826 Solving 2.5 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.062177826 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.062177826 + -2.5 x = -6.062177826 + -2.5 Combine like terms: -6.062177826 + -2.5 = -8.562177826 x = -8.562177826 Simplifying x = -8.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.562177826, -8.562177826}
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