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Simplifying 2x2 + 25x + -9.1 = 0 Reorder the terms: -9.1 + 25x + 2x2 = 0 Solving -9.1 + 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'. -4.55 + 12.5x + x2 = 0 Move the constant term to the right: Add '4.55' to each side of the equation. -4.55 + 12.5x + 4.55 + x2 = 0 + 4.55 Reorder the terms: -4.55 + 4.55 + 12.5x + x2 = 0 + 4.55 Combine like terms: -4.55 + 4.55 = 0.00 0.00 + 12.5x + x2 = 0 + 4.55 12.5x + x2 = 0 + 4.55 Combine like terms: 0 + 4.55 = 4.55 12.5x + x2 = 4.55 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 = 4.55 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 4.55 + 39.0625 Combine like terms: 4.55 + 39.0625 = 43.6125 39.0625 + 12.5x + x2 = 43.6125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 43.6125 Calculate the square root of the right side: 6.603976075 Break this problem into two subproblems by setting (x + 6.25) equal to 6.603976075 and -6.603976075.Subproblem 1
x + 6.25 = 6.603976075 Simplifying x + 6.25 = 6.603976075 Reorder the terms: 6.25 + x = 6.603976075 Solving 6.25 + x = 6.603976075 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 = 6.603976075 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.603976075 + -6.25 x = 6.603976075 + -6.25 Combine like terms: 6.603976075 + -6.25 = 0.353976075 x = 0.353976075 Simplifying x = 0.353976075Subproblem 2
x + 6.25 = -6.603976075 Simplifying x + 6.25 = -6.603976075 Reorder the terms: 6.25 + x = -6.603976075 Solving 6.25 + x = -6.603976075 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 = -6.603976075 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.603976075 + -6.25 x = -6.603976075 + -6.25 Combine like terms: -6.603976075 + -6.25 = -12.853976075 x = -12.853976075 Simplifying x = -12.853976075Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.353976075, -12.853976075}
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