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Simplifying 2x2 + 25x + 54 = 0 Reorder the terms: 54 + 25x + 2x2 = 0 Solving 54 + 25x + 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'. 27 + 12.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 12.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 12.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 12.5x + x2 = 0 + -27 12.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 12.5x + x2 = -27 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = -27 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -27 + 39.0625 Combine like terms: -27 + 39.0625 = 12.0625 39.0625 + 12.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 6.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 6.25 = 3.473110997 Simplifying x + 6.25 = 3.473110997 Reorder the terms: 6.25 + x = 3.473110997 Solving 6.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 3.473110997 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 3.473110997 + -6.25 x = 3.473110997 + -6.25 Combine like terms: 3.473110997 + -6.25 = -2.776889003 x = -2.776889003 Simplifying x = -2.776889003Subproblem 2
x + 6.25 = -3.473110997 Simplifying x + 6.25 = -3.473110997 Reorder the terms: 6.25 + x = -3.473110997 Solving 6.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -3.473110997 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -3.473110997 + -6.25 x = -3.473110997 + -6.25 Combine like terms: -3.473110997 + -6.25 = -9.723110997 x = -9.723110997 Simplifying x = -9.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.776889003, -9.723110997}
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