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Simplifying 2x2 + -55x + -35 = 0 Reorder the terms: -35 + -55x + 2x2 = 0 Solving -35 + -55x + 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'. -17.5 + -27.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -27.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -27.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -27.5x + x2 = 0 + 17.5 -27.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -27.5x + x2 = 17.5 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = 17.5 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 17.5 + 189.0625 Combine like terms: 17.5 + 189.0625 = 206.5625 189.0625 + -27.5x + x2 = 206.5625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 206.5625 Calculate the square root of the right side: 14.372282352 Break this problem into two subproblems by setting (x + -13.75) equal to 14.372282352 and -14.372282352.Subproblem 1
x + -13.75 = 14.372282352 Simplifying x + -13.75 = 14.372282352 Reorder the terms: -13.75 + x = 14.372282352 Solving -13.75 + x = 14.372282352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 14.372282352 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 14.372282352 + 13.75 x = 14.372282352 + 13.75 Combine like terms: 14.372282352 + 13.75 = 28.122282352 x = 28.122282352 Simplifying x = 28.122282352Subproblem 2
x + -13.75 = -14.372282352 Simplifying x + -13.75 = -14.372282352 Reorder the terms: -13.75 + x = -14.372282352 Solving -13.75 + x = -14.372282352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -14.372282352 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -14.372282352 + 13.75 x = -14.372282352 + 13.75 Combine like terms: -14.372282352 + 13.75 = -0.622282352 x = -0.622282352 Simplifying x = -0.622282352Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.122282352, -0.622282352}
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