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Simplifying 2x2 + -9x + -41 = 0 Reorder the terms: -41 + -9x + 2x2 = 0 Solving -41 + -9x + 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 + -4.5x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + -4.5x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + -4.5x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + -4.5x + x2 = 0 + 20.5 -4.5x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 -4.5x + x2 = 20.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 20.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 20.5 + 5.0625 Combine like terms: 20.5 + 5.0625 = 25.5625 5.0625 + -4.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -2.25) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -2.25 = 5.055937104 Simplifying x + -2.25 = 5.055937104 Reorder the terms: -2.25 + x = 5.055937104 Solving -2.25 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 5.055937104 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.055937104 + 2.25 x = 5.055937104 + 2.25 Combine like terms: 5.055937104 + 2.25 = 7.305937104 x = 7.305937104 Simplifying x = 7.305937104Subproblem 2
x + -2.25 = -5.055937104 Simplifying x + -2.25 = -5.055937104 Reorder the terms: -2.25 + x = -5.055937104 Solving -2.25 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -5.055937104 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.055937104 + 2.25 x = -5.055937104 + 2.25 Combine like terms: -5.055937104 + 2.25 = -2.805937104 x = -2.805937104 Simplifying x = -2.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.305937104, -2.805937104}
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