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Simplifying x(325 + 5x) = 3160 (325 * x + 5x * x) = 3160 (325x + 5x2) = 3160 Solving 325x + 5x2 = 3160 Solving for variable 'x'. Reorder the terms: -3160 + 325x + 5x2 = 3160 + -3160 Combine like terms: 3160 + -3160 = 0 -3160 + 325x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-632 + 65x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-632 + 65x + x2)' equal to zero and attempt to solve: Simplifying -632 + 65x + x2 = 0 Solving -632 + 65x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '632' to each side of the equation. -632 + 65x + 632 + x2 = 0 + 632 Reorder the terms: -632 + 632 + 65x + x2 = 0 + 632 Combine like terms: -632 + 632 = 0 0 + 65x + x2 = 0 + 632 65x + x2 = 0 + 632 Combine like terms: 0 + 632 = 632 65x + x2 = 632 The x term is 65x. Take half its coefficient (32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. 65x + 1056.25 + x2 = 632 + 1056.25 Reorder the terms: 1056.25 + 65x + x2 = 632 + 1056.25 Combine like terms: 632 + 1056.25 = 1688.25 1056.25 + 65x + x2 = 1688.25 Factor a perfect square on the left side: (x + 32.5)(x + 32.5) = 1688.25 Calculate the square root of the right side: 41.088319508 Break this problem into two subproblems by setting (x + 32.5) equal to 41.088319508 and -41.088319508.Subproblem 1
x + 32.5 = 41.088319508 Simplifying x + 32.5 = 41.088319508 Reorder the terms: 32.5 + x = 41.088319508 Solving 32.5 + x = 41.088319508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = 41.088319508 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = 41.088319508 + -32.5 x = 41.088319508 + -32.5 Combine like terms: 41.088319508 + -32.5 = 8.588319508 x = 8.588319508 Simplifying x = 8.588319508Subproblem 2
x + 32.5 = -41.088319508 Simplifying x + 32.5 = -41.088319508 Reorder the terms: 32.5 + x = -41.088319508 Solving 32.5 + x = -41.088319508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = -41.088319508 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = -41.088319508 + -32.5 x = -41.088319508 + -32.5 Combine like terms: -41.088319508 + -32.5 = -73.588319508 x = -73.588319508 Simplifying x = -73.588319508Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.588319508, -73.588319508}Solution
x = {8.588319508, -73.588319508}
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