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Simplifying 0 = x2 + 17x + -96 Reorder the terms: 0 = -96 + 17x + x2 Solving 0 = -96 + 17x + x2 Solving for variable 'x'. Combine like terms: 0 + 96 = 96 96 + -17x + -1x2 = -96 + 17x + x2 + 96 + -17x + -1x2 Reorder the terms: 96 + -17x + -1x2 = -96 + 96 + 17x + -17x + x2 + -1x2 Combine like terms: -96 + 96 = 0 96 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2 96 + -17x + -1x2 = 17x + -17x + x2 + -1x2 Combine like terms: 17x + -17x = 0 96 + -17x + -1x2 = 0 + x2 + -1x2 96 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 96 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 17x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 17x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 17x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 17x + x2 = 0 + 96 17x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 17x + x2 = 96 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 = 96 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 96 + 72.25 Combine like terms: 96 + 72.25 = 168.25 72.25 + 17x + x2 = 168.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 168.25 Calculate the square root of the right side: 12.971121771 Break this problem into two subproblems by setting (x + 8.5) equal to 12.971121771 and -12.971121771.Subproblem 1
x + 8.5 = 12.971121771 Simplifying x + 8.5 = 12.971121771 Reorder the terms: 8.5 + x = 12.971121771 Solving 8.5 + x = 12.971121771 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 = 12.971121771 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 12.971121771 + -8.5 x = 12.971121771 + -8.5 Combine like terms: 12.971121771 + -8.5 = 4.471121771 x = 4.471121771 Simplifying x = 4.471121771Subproblem 2
x + 8.5 = -12.971121771 Simplifying x + 8.5 = -12.971121771 Reorder the terms: 8.5 + x = -12.971121771 Solving 8.5 + x = -12.971121771 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 = -12.971121771 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -12.971121771 + -8.5 x = -12.971121771 + -8.5 Combine like terms: -12.971121771 + -8.5 = -21.471121771 x = -21.471121771 Simplifying x = -21.471121771Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.471121771, -21.471121771}
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