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Simplifying 272x2 + -2599x + 1279 = 0 Reorder the terms: 1279 + -2599x + 272x2 = 0 Solving 1279 + -2599x + 272x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 272 the coefficient of the squared term: Divide each side by '272'. 4.702205882 + -9.555147059x + x2 = 0 Move the constant term to the right: Add '-4.702205882' to each side of the equation. 4.702205882 + -9.555147059x + -4.702205882 + x2 = 0 + -4.702205882 Reorder the terms: 4.702205882 + -4.702205882 + -9.555147059x + x2 = 0 + -4.702205882 Combine like terms: 4.702205882 + -4.702205882 = 0.000000000 0.000000000 + -9.555147059x + x2 = 0 + -4.702205882 -9.555147059x + x2 = 0 + -4.702205882 Combine like terms: 0 + -4.702205882 = -4.702205882 -9.555147059x + x2 = -4.702205882 The x term is -9.555147059x. Take half its coefficient (-4.77757353). Square it (22.82520883) and add it to both sides. Add '22.82520883' to each side of the equation. -9.555147059x + 22.82520883 + x2 = -4.702205882 + 22.82520883 Reorder the terms: 22.82520883 + -9.555147059x + x2 = -4.702205882 + 22.82520883 Combine like terms: -4.702205882 + 22.82520883 = 18.123002948 22.82520883 + -9.555147059x + x2 = 18.123002948 Factor a perfect square on the left side: (x + -4.77757353)(x + -4.77757353) = 18.123002948 Calculate the square root of the right side: 4.257112043 Break this problem into two subproblems by setting (x + -4.77757353) equal to 4.257112043 and -4.257112043.Subproblem 1
x + -4.77757353 = 4.257112043 Simplifying x + -4.77757353 = 4.257112043 Reorder the terms: -4.77757353 + x = 4.257112043 Solving -4.77757353 + x = 4.257112043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.77757353' to each side of the equation. -4.77757353 + 4.77757353 + x = 4.257112043 + 4.77757353 Combine like terms: -4.77757353 + 4.77757353 = 0.00000000 0.00000000 + x = 4.257112043 + 4.77757353 x = 4.257112043 + 4.77757353 Combine like terms: 4.257112043 + 4.77757353 = 9.034685573 x = 9.034685573 Simplifying x = 9.034685573Subproblem 2
x + -4.77757353 = -4.257112043 Simplifying x + -4.77757353 = -4.257112043 Reorder the terms: -4.77757353 + x = -4.257112043 Solving -4.77757353 + x = -4.257112043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.77757353' to each side of the equation. -4.77757353 + 4.77757353 + x = -4.257112043 + 4.77757353 Combine like terms: -4.77757353 + 4.77757353 = 0.00000000 0.00000000 + x = -4.257112043 + 4.77757353 x = -4.257112043 + 4.77757353 Combine like terms: -4.257112043 + 4.77757353 = 0.520461487 x = 0.520461487 Simplifying x = 0.520461487Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.034685573, 0.520461487}
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