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Simplifying 2x2 + -27x + 71 = 0 Reorder the terms: 71 + -27x + 2x2 = 0 Solving 71 + -27x + 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'. 35.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '-35.5' to each side of the equation. 35.5 + -13.5x + -35.5 + x2 = 0 + -35.5 Reorder the terms: 35.5 + -35.5 + -13.5x + x2 = 0 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + -13.5x + x2 = 0 + -35.5 -13.5x + x2 = 0 + -35.5 Combine like terms: 0 + -35.5 = -35.5 -13.5x + x2 = -35.5 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -35.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -35.5 + 45.5625 Combine like terms: -35.5 + 45.5625 = 10.0625 45.5625 + -13.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -6.75) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -6.75 = 3.172144385 Simplifying x + -6.75 = 3.172144385 Reorder the terms: -6.75 + x = 3.172144385 Solving -6.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 3.172144385 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 3.172144385 + 6.75 x = 3.172144385 + 6.75 Combine like terms: 3.172144385 + 6.75 = 9.922144385 x = 9.922144385 Simplifying x = 9.922144385Subproblem 2
x + -6.75 = -3.172144385 Simplifying x + -6.75 = -3.172144385 Reorder the terms: -6.75 + x = -3.172144385 Solving -6.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -3.172144385 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -3.172144385 + 6.75 x = -3.172144385 + 6.75 Combine like terms: -3.172144385 + 6.75 = 3.577855615 x = 3.577855615 Simplifying x = 3.577855615Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.922144385, 3.577855615}
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