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Simplifying (x + -5)(2x + -5) = 95 Reorder the terms: (-5 + x)(2x + -5) = 95 Reorder the terms: (-5 + x)(-5 + 2x) = 95 Multiply (-5 + x) * (-5 + 2x) (-5(-5 + 2x) + x(-5 + 2x)) = 95 ((-5 * -5 + 2x * -5) + x(-5 + 2x)) = 95 ((25 + -10x) + x(-5 + 2x)) = 95 (25 + -10x + (-5 * x + 2x * x)) = 95 (25 + -10x + (-5x + 2x2)) = 95 Combine like terms: -10x + -5x = -15x (25 + -15x + 2x2) = 95 Solving 25 + -15x + 2x2 = 95 Solving for variable 'x'. Reorder the terms: 25 + -95 + -15x + 2x2 = 95 + -95 Combine like terms: 25 + -95 = -70 -70 + -15x + 2x2 = 95 + -95 Combine like terms: 95 + -95 = 0 -70 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -35 + -7.5x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -7.5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -7.5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -7.5x + x2 = 0 + 35 -7.5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -7.5x + x2 = 35 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 35 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 35 + 14.0625 Combine like terms: 35 + 14.0625 = 49.0625 14.0625 + -7.5x + x2 = 49.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 49.0625 Calculate the square root of the right side: 7.004462863 Break this problem into two subproblems by setting (x + -3.75) equal to 7.004462863 and -7.004462863.Subproblem 1
x + -3.75 = 7.004462863 Simplifying x + -3.75 = 7.004462863 Reorder the terms: -3.75 + x = 7.004462863 Solving -3.75 + x = 7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.004462863 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.004462863 + 3.75 x = 7.004462863 + 3.75 Combine like terms: 7.004462863 + 3.75 = 10.754462863 x = 10.754462863 Simplifying x = 10.754462863Subproblem 2
x + -3.75 = -7.004462863 Simplifying x + -3.75 = -7.004462863 Reorder the terms: -3.75 + x = -7.004462863 Solving -3.75 + x = -7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.004462863 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.004462863 + 3.75 x = -7.004462863 + 3.75 Combine like terms: -7.004462863 + 3.75 = -3.254462863 x = -3.254462863 Simplifying x = -3.254462863Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.754462863, -3.254462863}
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