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Simplifying 2x2 + -55x = 12 Reorder the terms: -55x + 2x2 = 12 Solving -55x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -55x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -55x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -27.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -27.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -27.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -27.5x + x2 = 0 + 6 -27.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -27.5x + x2 = 6 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 = 6 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 6 + 189.0625 Combine like terms: 6 + 189.0625 = 195.0625 189.0625 + -27.5x + x2 = 195.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 195.0625 Calculate the square root of the right side: 13.966477723 Break this problem into two subproblems by setting (x + -13.75) equal to 13.966477723 and -13.966477723.Subproblem 1
x + -13.75 = 13.966477723 Simplifying x + -13.75 = 13.966477723 Reorder the terms: -13.75 + x = 13.966477723 Solving -13.75 + x = 13.966477723 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 = 13.966477723 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 13.966477723 + 13.75 x = 13.966477723 + 13.75 Combine like terms: 13.966477723 + 13.75 = 27.716477723 x = 27.716477723 Simplifying x = 27.716477723Subproblem 2
x + -13.75 = -13.966477723 Simplifying x + -13.75 = -13.966477723 Reorder the terms: -13.75 + x = -13.966477723 Solving -13.75 + x = -13.966477723 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 = -13.966477723 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -13.966477723 + 13.75 x = -13.966477723 + 13.75 Combine like terms: -13.966477723 + 13.75 = -0.216477723 x = -0.216477723 Simplifying x = -0.216477723Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.716477723, -0.216477723}
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