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Simplifying 2x2 + -22x + -55 = 0 Reorder the terms: -55 + -22x + 2x2 = 0 Solving -55 + -22x + 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'. -27.5 + -11x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -11x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -11x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -11x + x2 = 0 + 27.5 -11x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -11x + x2 = 27.5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 27.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 27.5 + 30.25 Combine like terms: 27.5 + 30.25 = 57.75 30.25 + -11x + x2 = 57.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 57.75 Calculate the square root of the right side: 7.599342077 Break this problem into two subproblems by setting (x + -5.5) equal to 7.599342077 and -7.599342077.Subproblem 1
x + -5.5 = 7.599342077 Simplifying x + -5.5 = 7.599342077 Reorder the terms: -5.5 + x = 7.599342077 Solving -5.5 + x = 7.599342077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.599342077 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.599342077 + 5.5 x = 7.599342077 + 5.5 Combine like terms: 7.599342077 + 5.5 = 13.099342077 x = 13.099342077 Simplifying x = 13.099342077Subproblem 2
x + -5.5 = -7.599342077 Simplifying x + -5.5 = -7.599342077 Reorder the terms: -5.5 + x = -7.599342077 Solving -5.5 + x = -7.599342077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.599342077 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.599342077 + 5.5 x = -7.599342077 + 5.5 Combine like terms: -7.599342077 + 5.5 = -2.099342077 x = -2.099342077 Simplifying x = -2.099342077Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.099342077, -2.099342077}
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