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Simplifying 2x2 + 37x + 59 = 0 Reorder the terms: 59 + 37x + 2x2 = 0 Solving 59 + 37x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 29.5 + 18.5x + x2 = 0 Move the constant term to the right: Add '-29.5' to each side of the equation. 29.5 + 18.5x + -29.5 + x2 = 0 + -29.5 Reorder the terms: 29.5 + -29.5 + 18.5x + x2 = 0 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + 18.5x + x2 = 0 + -29.5 18.5x + x2 = 0 + -29.5 Combine like terms: 0 + -29.5 = -29.5 18.5x + x2 = -29.5 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 = -29.5 + 85.5625 Reorder the terms: 85.5625 + 18.5x + x2 = -29.5 + 85.5625 Combine like terms: -29.5 + 85.5625 = 56.0625 85.5625 + 18.5x + x2 = 56.0625 Factor a perfect square on the left side: (x + 9.25)(x + 9.25) = 56.0625 Calculate the square root of the right side: 7.487489566 Break this problem into two subproblems by setting (x + 9.25) equal to 7.487489566 and -7.487489566.Subproblem 1
x + 9.25 = 7.487489566 Simplifying x + 9.25 = 7.487489566 Reorder the terms: 9.25 + x = 7.487489566 Solving 9.25 + x = 7.487489566 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 = 7.487489566 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = 7.487489566 + -9.25 x = 7.487489566 + -9.25 Combine like terms: 7.487489566 + -9.25 = -1.762510434 x = -1.762510434 Simplifying x = -1.762510434Subproblem 2
x + 9.25 = -7.487489566 Simplifying x + 9.25 = -7.487489566 Reorder the terms: 9.25 + x = -7.487489566 Solving 9.25 + x = -7.487489566 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 = -7.487489566 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = -7.487489566 + -9.25 x = -7.487489566 + -9.25 Combine like terms: -7.487489566 + -9.25 = -16.737489566 x = -16.737489566 Simplifying x = -16.737489566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.762510434, -16.737489566}
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