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Simplifying 0.1x2 + 5x + 2.6 = 0 Reorder the terms: 2.6 + 5x + 0.1x2 = 0 Solving 2.6 + 5x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 26 + 50x + x2 = 0 Move the constant term to the right: Add '-26' to each side of the equation. 26 + 50x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 50x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 50x + x2 = 0 + -26 50x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 50x + x2 = -26 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = -26 + 625 Reorder the terms: 625 + 50x + x2 = -26 + 625 Combine like terms: -26 + 625 = 599 625 + 50x + x2 = 599 Factor a perfect square on the left side: (x + 25)(x + 25) = 599 Calculate the square root of the right side: 24.474476501 Break this problem into two subproblems by setting (x + 25) equal to 24.474476501 and -24.474476501.Subproblem 1
x + 25 = 24.474476501 Simplifying x + 25 = 24.474476501 Reorder the terms: 25 + x = 24.474476501 Solving 25 + x = 24.474476501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 24.474476501 + -25 Combine like terms: 25 + -25 = 0 0 + x = 24.474476501 + -25 x = 24.474476501 + -25 Combine like terms: 24.474476501 + -25 = -0.525523499 x = -0.525523499 Simplifying x = -0.525523499Subproblem 2
x + 25 = -24.474476501 Simplifying x + 25 = -24.474476501 Reorder the terms: 25 + x = -24.474476501 Solving 25 + x = -24.474476501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -24.474476501 + -25 Combine like terms: 25 + -25 = 0 0 + x = -24.474476501 + -25 x = -24.474476501 + -25 Combine like terms: -24.474476501 + -25 = -49.474476501 x = -49.474476501 Simplifying x = -49.474476501Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.525523499, -49.474476501}
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