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Simplifying -1x2 + 10x + 17 = 0 Reorder the terms: 17 + 10x + -1x2 = 0 Solving 17 + 10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -10x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -10x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -10x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -10x + x2 = 0 + 17 -10x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -10x + x2 = 17 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 17 + 25 Reorder the terms: 25 + -10x + x2 = 17 + 25 Combine like terms: 17 + 25 = 42 25 + -10x + x2 = 42 Factor a perfect square on the left side: (x + -5)(x + -5) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + -5) equal to 6.480740698 and -6.480740698.Subproblem 1
x + -5 = 6.480740698 Simplifying x + -5 = 6.480740698 Reorder the terms: -5 + x = 6.480740698 Solving -5 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.480740698 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.480740698 + 5 x = 6.480740698 + 5 Combine like terms: 6.480740698 + 5 = 11.480740698 x = 11.480740698 Simplifying x = 11.480740698Subproblem 2
x + -5 = -6.480740698 Simplifying x + -5 = -6.480740698 Reorder the terms: -5 + x = -6.480740698 Solving -5 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.480740698 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.480740698 + 5 x = -6.480740698 + 5 Combine like terms: -6.480740698 + 5 = -1.480740698 x = -1.480740698 Simplifying x = -1.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.480740698, -1.480740698}
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