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Simplifying 2x2 + 37x = 1 Reorder the terms: 37x + 2x2 = 1 Solving 37x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 37x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 37x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 18.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 18.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 18.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 18.5x + x2 = 0 + 0.5 18.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 18.5x + x2 = 0.5 The x term is 18.5x. Take half its coefficient (9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. 18.5x + 85.5625 + x2 = 0.5 + 85.5625 Reorder the terms: 85.5625 + 18.5x + x2 = 0.5 + 85.5625 Combine like terms: 0.5 + 85.5625 = 86.0625 85.5625 + 18.5x + x2 = 86.0625 Factor a perfect square on the left side: (x + 9.25)(x + 9.25) = 86.0625 Calculate the square root of the right side: 9.276987658 Break this problem into two subproblems by setting (x + 9.25) equal to 9.276987658 and -9.276987658.Subproblem 1
x + 9.25 = 9.276987658 Simplifying x + 9.25 = 9.276987658 Reorder the terms: 9.25 + x = 9.276987658 Solving 9.25 + x = 9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = 9.276987658 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = 9.276987658 + -9.25 x = 9.276987658 + -9.25 Combine like terms: 9.276987658 + -9.25 = 0.026987658 x = 0.026987658 Simplifying x = 0.026987658Subproblem 2
x + 9.25 = -9.276987658 Simplifying x + 9.25 = -9.276987658 Reorder the terms: 9.25 + x = -9.276987658 Solving 9.25 + x = -9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = -9.276987658 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = -9.276987658 + -9.25 x = -9.276987658 + -9.25 Combine like terms: -9.276987658 + -9.25 = -18.526987658 x = -18.526987658 Simplifying x = -18.526987658Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.026987658, -18.526987658}
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