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Simplifying 2x2 + 5x + -41 = 0 Reorder the terms: -41 + 5x + 2x2 = 0 Solving -41 + 5x + 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'. -20.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 2.5x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 2.5x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 2.5x + x2 = 0 + 20.5 2.5x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 2.5x + x2 = 20.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 20.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 20.5 + 1.5625 Combine like terms: 20.5 + 1.5625 = 22.0625 1.5625 + 2.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 1.25) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 1.25 = 4.697073557 Simplifying x + 1.25 = 4.697073557 Reorder the terms: 1.25 + x = 4.697073557 Solving 1.25 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.697073557 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.697073557 + -1.25 x = 4.697073557 + -1.25 Combine like terms: 4.697073557 + -1.25 = 3.447073557 x = 3.447073557 Simplifying x = 3.447073557Subproblem 2
x + 1.25 = -4.697073557 Simplifying x + 1.25 = -4.697073557 Reorder the terms: 1.25 + x = -4.697073557 Solving 1.25 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.697073557 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.697073557 + -1.25 x = -4.697073557 + -1.25 Combine like terms: -4.697073557 + -1.25 = -5.947073557 x = -5.947073557 Simplifying x = -5.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.447073557, -5.947073557}
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