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Simplifying (2x2) + -17x + -10 = 0 Reorder the terms: -10 + -17x + (2x2) = 0 Solving -10 + -17x + (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'. -5 + -8.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -8.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.5x + x2 = 0 + 5 -8.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.5x + x2 = 5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 5 + 18.0625 Combine like terms: 5 + 18.0625 = 23.0625 18.0625 + -8.5x + x2 = 23.0625 Factor a perfect square on the left side: ((x) + -4.25)((x) + -4.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting ((x) + -4.25) equal to 4.802343178 and -4.802343178.Subproblem 1
(x) + -4.25 = 4.802343178 Simplifying (x) + -4.25 = 4.802343178 x + -4.25 = 4.802343178 Reorder the terms: -4.25 + x = 4.802343178 Solving -4.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.802343178 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.802343178 + 4.25 x = 4.802343178 + 4.25 Combine like terms: 4.802343178 + 4.25 = 9.052343178 x = 9.052343178 Simplifying x = 9.052343178Subproblem 2
(x) + -4.25 = -4.802343178 Simplifying (x) + -4.25 = -4.802343178 x + -4.25 = -4.802343178 Reorder the terms: -4.25 + x = -4.802343178 Solving -4.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.802343178 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.802343178 + 4.25 x = -4.802343178 + 4.25 Combine like terms: -4.802343178 + 4.25 = -0.552343178 x = -0.552343178 Simplifying x = -0.552343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.052343178, -0.552343178}
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