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Simplifying -1x2 + -5x = -96 Reorder the terms: -5x + -1x2 = -96 Solving -5x + -1x2 = -96 Solving for variable 'x'. Reorder the terms: 96 + -5x + -1x2 = -96 + 96 Combine like terms: -96 + 96 = 0 96 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 5x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 5x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 5x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 5x + x2 = 0 + 96 5x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 5x + x2 = 96 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 96 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 96 + 6.25 Combine like terms: 96 + 6.25 = 102.25 6.25 + 5x + x2 = 102.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + 2.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + 2.5 = 10.111874208 Simplifying x + 2.5 = 10.111874208 Reorder the terms: 2.5 + x = 10.111874208 Solving 2.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.111874208 + -2.5 x = 10.111874208 + -2.5 Combine like terms: 10.111874208 + -2.5 = 7.611874208 x = 7.611874208 Simplifying x = 7.611874208Subproblem 2
x + 2.5 = -10.111874208 Simplifying x + 2.5 = -10.111874208 Reorder the terms: 2.5 + x = -10.111874208 Solving 2.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.111874208 + -2.5 x = -10.111874208 + -2.5 Combine like terms: -10.111874208 + -2.5 = -12.611874208 x = -12.611874208 Simplifying x = -12.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.611874208, -12.611874208}
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