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Simplifying 2.75x2 + -36x + 11 = 0 Reorder the terms: 11 + -36x + 2.75x2 = 0 Solving 11 + -36x + 2.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.75 the coefficient of the squared term: Divide each side by '2.75'. 4 + -13.09090909x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -13.09090909x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -13.09090909x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13.09090909x + x2 = 0 + -4 -13.09090909x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -13.09090909x + x2 = -4 The x term is -13.09090909x. Take half its coefficient (-6.545454545). Square it (42.84297520) and add it to both sides. Add '42.84297520' to each side of the equation. -13.09090909x + 42.84297520 + x2 = -4 + 42.84297520 Reorder the terms: 42.84297520 + -13.09090909x + x2 = -4 + 42.84297520 Combine like terms: -4 + 42.84297520 = 38.8429752 42.84297520 + -13.09090909x + x2 = 38.8429752 Factor a perfect square on the left side: (x + -6.545454545)(x + -6.545454545) = 38.8429752 Calculate the square root of the right side: 6.232413273 Break this problem into two subproblems by setting (x + -6.545454545) equal to 6.232413273 and -6.232413273.Subproblem 1
x + -6.545454545 = 6.232413273 Simplifying x + -6.545454545 = 6.232413273 Reorder the terms: -6.545454545 + x = 6.232413273 Solving -6.545454545 + x = 6.232413273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.545454545' to each side of the equation. -6.545454545 + 6.545454545 + x = 6.232413273 + 6.545454545 Combine like terms: -6.545454545 + 6.545454545 = 0.000000000 0.000000000 + x = 6.232413273 + 6.545454545 x = 6.232413273 + 6.545454545 Combine like terms: 6.232413273 + 6.545454545 = 12.777867818 x = 12.777867818 Simplifying x = 12.777867818Subproblem 2
x + -6.545454545 = -6.232413273 Simplifying x + -6.545454545 = -6.232413273 Reorder the terms: -6.545454545 + x = -6.232413273 Solving -6.545454545 + x = -6.232413273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.545454545' to each side of the equation. -6.545454545 + 6.545454545 + x = -6.232413273 + 6.545454545 Combine like terms: -6.545454545 + 6.545454545 = 0.000000000 0.000000000 + x = -6.232413273 + 6.545454545 x = -6.232413273 + 6.545454545 Combine like terms: -6.232413273 + 6.545454545 = 0.313041272 x = 0.313041272 Simplifying x = 0.313041272Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.777867818, 0.313041272}
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