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Simplifying 0 = x2 + 17x + -2 Reorder the terms: 0 = -2 + 17x + x2 Solving 0 = -2 + 17x + x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -17x + -1x2 = -2 + 17x + x2 + 2 + -17x + -1x2 Reorder the terms: 2 + -17x + -1x2 = -2 + 2 + 17x + -17x + x2 + -1x2 Combine like terms: -2 + 2 = 0 2 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2 2 + -17x + -1x2 = 17x + -17x + x2 + -1x2 Combine like terms: 17x + -17x = 0 2 + -17x + -1x2 = 0 + x2 + -1x2 2 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 17x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 17x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 17x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 17x + x2 = 0 + 2 17x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 17x + x2 = 2 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 2 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 2 + 72.25 Combine like terms: 2 + 72.25 = 74.25 72.25 + 17x + x2 = 74.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + 8.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + 8.5 = 8.61684397 Simplifying x + 8.5 = 8.61684397 Reorder the terms: 8.5 + x = 8.61684397 Solving 8.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.61684397 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.61684397 + -8.5 x = 8.61684397 + -8.5 Combine like terms: 8.61684397 + -8.5 = 0.11684397 x = 0.11684397 Simplifying x = 0.11684397Subproblem 2
x + 8.5 = -8.61684397 Simplifying x + 8.5 = -8.61684397 Reorder the terms: 8.5 + x = -8.61684397 Solving 8.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.61684397 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.61684397 + -8.5 x = -8.61684397 + -8.5 Combine like terms: -8.61684397 + -8.5 = -17.11684397 x = -17.11684397 Simplifying x = -17.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.11684397, -17.11684397}
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