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Simplifying (5x + -25)(2x + 2) = x Reorder the terms: (-25 + 5x)(2x + 2) = x Reorder the terms: (-25 + 5x)(2 + 2x) = x Multiply (-25 + 5x) * (2 + 2x) (-25(2 + 2x) + 5x * (2 + 2x)) = x ((2 * -25 + 2x * -25) + 5x * (2 + 2x)) = x ((-50 + -50x) + 5x * (2 + 2x)) = x (-50 + -50x + (2 * 5x + 2x * 5x)) = x (-50 + -50x + (10x + 10x2)) = x Combine like terms: -50x + 10x = -40x (-50 + -40x + 10x2) = x Solving -50 + -40x + 10x2 = x Solving for variable 'x'. Reorder the terms: -50 + -40x + -1x + 10x2 = x + -1x Combine like terms: -40x + -1x = -41x -50 + -41x + 10x2 = x + -1x Combine like terms: x + -1x = 0 -50 + -41x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5 + -4.1x + x2 = 0.0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.1x + 5 + x2 = 0.0 + 5 Reorder the terms: -5 + 5 + -4.1x + x2 = 0.0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.1x + x2 = 0.0 + 5 -4.1x + x2 = 0.0 + 5 Combine like terms: 0.0 + 5 = 5 -4.1x + x2 = 5 The x term is -4.1x. Take half its coefficient (-2.05). Square it (4.2025) and add it to both sides. Add '4.2025' to each side of the equation. -4.1x + 4.2025 + x2 = 5 + 4.2025 Reorder the terms: 4.2025 + -4.1x + x2 = 5 + 4.2025 Combine like terms: 5 + 4.2025 = 9.2025 4.2025 + -4.1x + x2 = 9.2025 Factor a perfect square on the left side: (x + -2.05)(x + -2.05) = 9.2025 Calculate the square root of the right side: 3.033562262 Break this problem into two subproblems by setting (x + -2.05) equal to 3.033562262 and -3.033562262.Subproblem 1
x + -2.05 = 3.033562262 Simplifying x + -2.05 = 3.033562262 Reorder the terms: -2.05 + x = 3.033562262 Solving -2.05 + x = 3.033562262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.05' to each side of the equation. -2.05 + 2.05 + x = 3.033562262 + 2.05 Combine like terms: -2.05 + 2.05 = 0.00 0.00 + x = 3.033562262 + 2.05 x = 3.033562262 + 2.05 Combine like terms: 3.033562262 + 2.05 = 5.083562262 x = 5.083562262 Simplifying x = 5.083562262Subproblem 2
x + -2.05 = -3.033562262 Simplifying x + -2.05 = -3.033562262 Reorder the terms: -2.05 + x = -3.033562262 Solving -2.05 + x = -3.033562262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.05' to each side of the equation. -2.05 + 2.05 + x = -3.033562262 + 2.05 Combine like terms: -2.05 + 2.05 = 0.00 0.00 + x = -3.033562262 + 2.05 x = -3.033562262 + 2.05 Combine like terms: -3.033562262 + 2.05 = -0.983562262 x = -0.983562262 Simplifying x = -0.983562262Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.083562262, -0.983562262}
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