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Simplifying 61x2 + -44x + -2435 = 0 Reorder the terms: -2435 + -44x + 61x2 = 0 Solving -2435 + -44x + 61x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 61 the coefficient of the squared term: Divide each side by '61'. -39.91803279 + -0.7213114754x + x2 = 0 Move the constant term to the right: Add '39.91803279' to each side of the equation. -39.91803279 + -0.7213114754x + 39.91803279 + x2 = 0 + 39.91803279 Reorder the terms: -39.91803279 + 39.91803279 + -0.7213114754x + x2 = 0 + 39.91803279 Combine like terms: -39.91803279 + 39.91803279 = 0.00000000 0.00000000 + -0.7213114754x + x2 = 0 + 39.91803279 -0.7213114754x + x2 = 0 + 39.91803279 Combine like terms: 0 + 39.91803279 = 39.91803279 -0.7213114754x + x2 = 39.91803279 The x term is -0.7213114754x. Take half its coefficient (-0.3606557377). Square it (0.1300725611) and add it to both sides. Add '0.1300725611' to each side of the equation. -0.7213114754x + 0.1300725611 + x2 = 39.91803279 + 0.1300725611 Reorder the terms: 0.1300725611 + -0.7213114754x + x2 = 39.91803279 + 0.1300725611 Combine like terms: 39.91803279 + 0.1300725611 = 40.0481053511 0.1300725611 + -0.7213114754x + x2 = 40.0481053511 Factor a perfect square on the left side: (x + -0.3606557377)(x + -0.3606557377) = 40.0481053511 Calculate the square root of the right side: 6.32835724 Break this problem into two subproblems by setting (x + -0.3606557377) equal to 6.32835724 and -6.32835724.Subproblem 1
x + -0.3606557377 = 6.32835724 Simplifying x + -0.3606557377 = 6.32835724 Reorder the terms: -0.3606557377 + x = 6.32835724 Solving -0.3606557377 + x = 6.32835724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3606557377' to each side of the equation. -0.3606557377 + 0.3606557377 + x = 6.32835724 + 0.3606557377 Combine like terms: -0.3606557377 + 0.3606557377 = 0.0000000000 0.0000000000 + x = 6.32835724 + 0.3606557377 x = 6.32835724 + 0.3606557377 Combine like terms: 6.32835724 + 0.3606557377 = 6.6890129777 x = 6.6890129777 Simplifying x = 6.6890129777Subproblem 2
x + -0.3606557377 = -6.32835724 Simplifying x + -0.3606557377 = -6.32835724 Reorder the terms: -0.3606557377 + x = -6.32835724 Solving -0.3606557377 + x = -6.32835724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3606557377' to each side of the equation. -0.3606557377 + 0.3606557377 + x = -6.32835724 + 0.3606557377 Combine like terms: -0.3606557377 + 0.3606557377 = 0.0000000000 0.0000000000 + x = -6.32835724 + 0.3606557377 x = -6.32835724 + 0.3606557377 Combine like terms: -6.32835724 + 0.3606557377 = -5.9677015023 x = -5.9677015023 Simplifying x = -5.9677015023Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6890129777, -5.9677015023}
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