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Simplifying 2x2 + 25x + -39 = 0 Reorder the terms: -39 + 25x + 2x2 = 0 Solving -39 + 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'. -19.5 + 12.5x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + 12.5x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + 12.5x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + 12.5x + x2 = 0 + 19.5 12.5x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 12.5x + x2 = 19.5 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 = 19.5 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 19.5 + 39.0625 Combine like terms: 19.5 + 39.0625 = 58.5625 39.0625 + 12.5x + x2 = 58.5625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 58.5625 Calculate the square root of the right side: 7.652613933 Break this problem into two subproblems by setting (x + 6.25) equal to 7.652613933 and -7.652613933.Subproblem 1
x + 6.25 = 7.652613933 Simplifying x + 6.25 = 7.652613933 Reorder the terms: 6.25 + x = 7.652613933 Solving 6.25 + x = 7.652613933 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 = 7.652613933 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 7.652613933 + -6.25 x = 7.652613933 + -6.25 Combine like terms: 7.652613933 + -6.25 = 1.402613933 x = 1.402613933 Simplifying x = 1.402613933Subproblem 2
x + 6.25 = -7.652613933 Simplifying x + 6.25 = -7.652613933 Reorder the terms: 6.25 + x = -7.652613933 Solving 6.25 + x = -7.652613933 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 = -7.652613933 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -7.652613933 + -6.25 x = -7.652613933 + -6.25 Combine like terms: -7.652613933 + -6.25 = -13.902613933 x = -13.902613933 Simplifying x = -13.902613933Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.402613933, -13.902613933}
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