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Simplifying 33x2 + -136x + -17 = 0 Reorder the terms: -17 + -136x + 33x2 = 0 Solving -17 + -136x + 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'. -0.5151515152 + -4.121212121x + x2 = 0 Move the constant term to the right: Add '0.5151515152' to each side of the equation. -0.5151515152 + -4.121212121x + 0.5151515152 + x2 = 0 + 0.5151515152 Reorder the terms: -0.5151515152 + 0.5151515152 + -4.121212121x + x2 = 0 + 0.5151515152 Combine like terms: -0.5151515152 + 0.5151515152 = 0.0000000000 0.0000000000 + -4.121212121x + x2 = 0 + 0.5151515152 -4.121212121x + x2 = 0 + 0.5151515152 Combine like terms: 0 + 0.5151515152 = 0.5151515152 -4.121212121x + x2 = 0.5151515152 The x term is -4.121212121x. Take half its coefficient (-2.060606061). Square it (4.246097339) and add it to both sides. Add '4.246097339' to each side of the equation. -4.121212121x + 4.246097339 + x2 = 0.5151515152 + 4.246097339 Reorder the terms: 4.246097339 + -4.121212121x + x2 = 0.5151515152 + 4.246097339 Combine like terms: 0.5151515152 + 4.246097339 = 4.7612488542 4.246097339 + -4.121212121x + x2 = 4.7612488542 Factor a perfect square on the left side: (x + -2.060606061)(x + -2.060606061) = 4.7612488542 Calculate the square root of the right side: 2.18202861 Break this problem into two subproblems by setting (x + -2.060606061) equal to 2.18202861 and -2.18202861.Subproblem 1
x + -2.060606061 = 2.18202861 Simplifying x + -2.060606061 = 2.18202861 Reorder the terms: -2.060606061 + x = 2.18202861 Solving -2.060606061 + x = 2.18202861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.060606061' to each side of the equation. -2.060606061 + 2.060606061 + x = 2.18202861 + 2.060606061 Combine like terms: -2.060606061 + 2.060606061 = 0.000000000 0.000000000 + x = 2.18202861 + 2.060606061 x = 2.18202861 + 2.060606061 Combine like terms: 2.18202861 + 2.060606061 = 4.242634671 x = 4.242634671 Simplifying x = 4.242634671Subproblem 2
x + -2.060606061 = -2.18202861 Simplifying x + -2.060606061 = -2.18202861 Reorder the terms: -2.060606061 + x = -2.18202861 Solving -2.060606061 + x = -2.18202861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.060606061' to each side of the equation. -2.060606061 + 2.060606061 + x = -2.18202861 + 2.060606061 Combine like terms: -2.060606061 + 2.060606061 = 0.000000000 0.000000000 + x = -2.18202861 + 2.060606061 x = -2.18202861 + 2.060606061 Combine like terms: -2.18202861 + 2.060606061 = -0.121422549 x = -0.121422549 Simplifying x = -0.121422549Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.242634671, -0.121422549}
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