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Simplifying 2x2 + 25x + -8.9 = 0 Reorder the terms: -8.9 + 25x + 2x2 = 0 Solving -8.9 + 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'. -4.45 + 12.5x + x2 = 0 Move the constant term to the right: Add '4.45' to each side of the equation. -4.45 + 12.5x + 4.45 + x2 = 0 + 4.45 Reorder the terms: -4.45 + 4.45 + 12.5x + x2 = 0 + 4.45 Combine like terms: -4.45 + 4.45 = 0.00 0.00 + 12.5x + x2 = 0 + 4.45 12.5x + x2 = 0 + 4.45 Combine like terms: 0 + 4.45 = 4.45 12.5x + x2 = 4.45 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 = 4.45 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 4.45 + 39.0625 Combine like terms: 4.45 + 39.0625 = 43.5125 39.0625 + 12.5x + x2 = 43.5125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 43.5125 Calculate the square root of the right side: 6.596400534 Break this problem into two subproblems by setting (x + 6.25) equal to 6.596400534 and -6.596400534.Subproblem 1
x + 6.25 = 6.596400534 Simplifying x + 6.25 = 6.596400534 Reorder the terms: 6.25 + x = 6.596400534 Solving 6.25 + x = 6.596400534 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 = 6.596400534 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.596400534 + -6.25 x = 6.596400534 + -6.25 Combine like terms: 6.596400534 + -6.25 = 0.346400534 x = 0.346400534 Simplifying x = 0.346400534Subproblem 2
x + 6.25 = -6.596400534 Simplifying x + 6.25 = -6.596400534 Reorder the terms: 6.25 + x = -6.596400534 Solving 6.25 + x = -6.596400534 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 = -6.596400534 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.596400534 + -6.25 x = -6.596400534 + -6.25 Combine like terms: -6.596400534 + -6.25 = -12.846400534 x = -12.846400534 Simplifying x = -12.846400534Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.346400534, -12.846400534}
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