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Simplifying 2x2 + -35x + -6.5 = 0 Reorder the terms: -6.5 + -35x + 2x2 = 0 Solving -6.5 + -35x + 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'. -3.25 + -17.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -17.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -17.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -17.5x + x2 = 0 + 3.25 -17.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -17.5x + x2 = 3.25 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 3.25 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 3.25 + 76.5625 Combine like terms: 3.25 + 76.5625 = 79.8125 76.5625 + -17.5x + x2 = 79.8125 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 79.8125 Calculate the square root of the right side: 8.933784193 Break this problem into two subproblems by setting (x + -8.75) equal to 8.933784193 and -8.933784193.Subproblem 1
x + -8.75 = 8.933784193 Simplifying x + -8.75 = 8.933784193 Reorder the terms: -8.75 + x = 8.933784193 Solving -8.75 + x = 8.933784193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.933784193 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.933784193 + 8.75 x = 8.933784193 + 8.75 Combine like terms: 8.933784193 + 8.75 = 17.683784193 x = 17.683784193 Simplifying x = 17.683784193Subproblem 2
x + -8.75 = -8.933784193 Simplifying x + -8.75 = -8.933784193 Reorder the terms: -8.75 + x = -8.933784193 Solving -8.75 + x = -8.933784193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.933784193 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.933784193 + 8.75 x = -8.933784193 + 8.75 Combine like terms: -8.933784193 + 8.75 = -0.183784193 x = -0.183784193 Simplifying x = -0.183784193Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.683784193, -0.183784193}
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