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Simplifying x(x + -5) = 99 Reorder the terms: x(-5 + x) = 99 (-5 * x + x * x) = 99 (-5x + x2) = 99 Solving -5x + x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + -5x + x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -5x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -5x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -5x + x2 = 0 + 99 -5x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -5x + x2 = 99 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 = 99 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 99 + 6.25 Combine like terms: 99 + 6.25 = 105.25 6.25 + -5x + x2 = 105.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (x + -2.5) equal to 10.259142264 and -10.259142264.Subproblem 1
x + -2.5 = 10.259142264 Simplifying x + -2.5 = 10.259142264 Reorder the terms: -2.5 + x = 10.259142264 Solving -2.5 + x = 10.259142264 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 = 10.259142264 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.259142264 + 2.5 x = 10.259142264 + 2.5 Combine like terms: 10.259142264 + 2.5 = 12.759142264 x = 12.759142264 Simplifying x = 12.759142264Subproblem 2
x + -2.5 = -10.259142264 Simplifying x + -2.5 = -10.259142264 Reorder the terms: -2.5 + x = -10.259142264 Solving -2.5 + x = -10.259142264 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 = -10.259142264 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.259142264 + 2.5 x = -10.259142264 + 2.5 Combine like terms: -10.259142264 + 2.5 = -7.759142264 x = -7.759142264 Simplifying x = -7.759142264Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.759142264, -7.759142264}
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