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Simplifying (x + -5)(2x + 5) = 119 Reorder the terms: (-5 + x)(2x + 5) = 119 Reorder the terms: (-5 + x)(5 + 2x) = 119 Multiply (-5 + x) * (5 + 2x) (-5(5 + 2x) + x(5 + 2x)) = 119 ((5 * -5 + 2x * -5) + x(5 + 2x)) = 119 ((-25 + -10x) + x(5 + 2x)) = 119 (-25 + -10x + (5 * x + 2x * x)) = 119 (-25 + -10x + (5x + 2x2)) = 119 Combine like terms: -10x + 5x = -5x (-25 + -5x + 2x2) = 119 Solving -25 + -5x + 2x2 = 119 Solving for variable 'x'. Reorder the terms: -25 + -119 + -5x + 2x2 = 119 + -119 Combine like terms: -25 + -119 = -144 -144 + -5x + 2x2 = 119 + -119 Combine like terms: 119 + -119 = 0 -144 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -72 + -2.5x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -2.5x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -2.5x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -2.5x + x2 = 0 + 72 -2.5x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -2.5x + x2 = 72 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 72 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 72 + 1.5625 Combine like terms: 72 + 1.5625 = 73.5625 1.5625 + -2.5x + x2 = 73.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 73.5625 Calculate the square root of the right side: 8.576858399 Break this problem into two subproblems by setting (x + -1.25) equal to 8.576858399 and -8.576858399.Subproblem 1
x + -1.25 = 8.576858399 Simplifying x + -1.25 = 8.576858399 Reorder the terms: -1.25 + x = 8.576858399 Solving -1.25 + x = 8.576858399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 8.576858399 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.576858399 + 1.25 x = 8.576858399 + 1.25 Combine like terms: 8.576858399 + 1.25 = 9.826858399 x = 9.826858399 Simplifying x = 9.826858399Subproblem 2
x + -1.25 = -8.576858399 Simplifying x + -1.25 = -8.576858399 Reorder the terms: -1.25 + x = -8.576858399 Solving -1.25 + x = -8.576858399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -8.576858399 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.576858399 + 1.25 x = -8.576858399 + 1.25 Combine like terms: -8.576858399 + 1.25 = -7.326858399 x = -7.326858399 Simplifying x = -7.326858399Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.826858399, -7.326858399}
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