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Simplifying -33x2 + 139x + -98 = 0 Reorder the terms: -98 + 139x + -33x2 = 0 Solving -98 + 139x + -33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -33 the coefficient of the squared term: Divide each side by '-33'. 2.96969697 + -4.212121212x + x2 = 0 Move the constant term to the right: Add '-2.96969697' to each side of the equation. 2.96969697 + -4.212121212x + -2.96969697 + x2 = 0 + -2.96969697 Reorder the terms: 2.96969697 + -2.96969697 + -4.212121212x + x2 = 0 + -2.96969697 Combine like terms: 2.96969697 + -2.96969697 = 0.00000000 0.00000000 + -4.212121212x + x2 = 0 + -2.96969697 -4.212121212x + x2 = 0 + -2.96969697 Combine like terms: 0 + -2.96969697 = -2.96969697 -4.212121212x + x2 = -2.96969697 The x term is -4.212121212x. Take half its coefficient (-2.106060606). Square it (4.435491276) and add it to both sides. Add '4.435491276' to each side of the equation. -4.212121212x + 4.435491276 + x2 = -2.96969697 + 4.435491276 Reorder the terms: 4.435491276 + -4.212121212x + x2 = -2.96969697 + 4.435491276 Combine like terms: -2.96969697 + 4.435491276 = 1.465794306 4.435491276 + -4.212121212x + x2 = 1.465794306 Factor a perfect square on the left side: (x + -2.106060606)(x + -2.106060606) = 1.465794306 Calculate the square root of the right side: 1.210699924 Break this problem into two subproblems by setting (x + -2.106060606) equal to 1.210699924 and -1.210699924.Subproblem 1
x + -2.106060606 = 1.210699924 Simplifying x + -2.106060606 = 1.210699924 Reorder the terms: -2.106060606 + x = 1.210699924 Solving -2.106060606 + x = 1.210699924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.106060606' to each side of the equation. -2.106060606 + 2.106060606 + x = 1.210699924 + 2.106060606 Combine like terms: -2.106060606 + 2.106060606 = 0.000000000 0.000000000 + x = 1.210699924 + 2.106060606 x = 1.210699924 + 2.106060606 Combine like terms: 1.210699924 + 2.106060606 = 3.31676053 x = 3.31676053 Simplifying x = 3.31676053Subproblem 2
x + -2.106060606 = -1.210699924 Simplifying x + -2.106060606 = -1.210699924 Reorder the terms: -2.106060606 + x = -1.210699924 Solving -2.106060606 + x = -1.210699924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.106060606' to each side of the equation. -2.106060606 + 2.106060606 + x = -1.210699924 + 2.106060606 Combine like terms: -2.106060606 + 2.106060606 = 0.000000000 0.000000000 + x = -1.210699924 + 2.106060606 x = -1.210699924 + 2.106060606 Combine like terms: -1.210699924 + 2.106060606 = 0.895360682 x = 0.895360682 Simplifying x = 0.895360682Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.31676053, 0.895360682}
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