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Simplifying 2x2 + 40x = 3201 Reorder the terms: 40x + 2x2 = 3201 Solving 40x + 2x2 = 3201 Solving for variable 'x'. Reorder the terms: -3201 + 40x + 2x2 = 3201 + -3201 Combine like terms: 3201 + -3201 = 0 -3201 + 40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1600.5 + 20x + x2 = 0 Move the constant term to the right: Add '1600.5' to each side of the equation. -1600.5 + 20x + 1600.5 + x2 = 0 + 1600.5 Reorder the terms: -1600.5 + 1600.5 + 20x + x2 = 0 + 1600.5 Combine like terms: -1600.5 + 1600.5 = 0.0 0.0 + 20x + x2 = 0 + 1600.5 20x + x2 = 0 + 1600.5 Combine like terms: 0 + 1600.5 = 1600.5 20x + x2 = 1600.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 1600.5 + 100 Reorder the terms: 100 + 20x + x2 = 1600.5 + 100 Combine like terms: 1600.5 + 100 = 1700.5 100 + 20x + x2 = 1700.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 1700.5 Calculate the square root of the right side: 41.237119201 Break this problem into two subproblems by setting (x + 10) equal to 41.237119201 and -41.237119201.Subproblem 1
x + 10 = 41.237119201 Simplifying x + 10 = 41.237119201 Reorder the terms: 10 + x = 41.237119201 Solving 10 + x = 41.237119201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 41.237119201 + -10 Combine like terms: 10 + -10 = 0 0 + x = 41.237119201 + -10 x = 41.237119201 + -10 Combine like terms: 41.237119201 + -10 = 31.237119201 x = 31.237119201 Simplifying x = 31.237119201Subproblem 2
x + 10 = -41.237119201 Simplifying x + 10 = -41.237119201 Reorder the terms: 10 + x = -41.237119201 Solving 10 + x = -41.237119201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -41.237119201 + -10 Combine like terms: 10 + -10 = 0 0 + x = -41.237119201 + -10 x = -41.237119201 + -10 Combine like terms: -41.237119201 + -10 = -51.237119201 x = -51.237119201 Simplifying x = -51.237119201Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.237119201, -51.237119201}
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