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Simplifying 2x2 + -2.2x + -2.7 = 0 Reorder the terms: -2.7 + -2.2x + 2x2 = 0 Solving -2.7 + -2.2x + 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'. -1.35 + -1.1x + x2 = 0 Move the constant term to the right: Add '1.35' to each side of the equation. -1.35 + -1.1x + 1.35 + x2 = 0 + 1.35 Reorder the terms: -1.35 + 1.35 + -1.1x + x2 = 0 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + -1.1x + x2 = 0 + 1.35 -1.1x + x2 = 0 + 1.35 Combine like terms: 0 + 1.35 = 1.35 -1.1x + x2 = 1.35 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 1.35 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 1.35 + 0.3025 Combine like terms: 1.35 + 0.3025 = 1.6525 0.3025 + -1.1x + x2 = 1.6525 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 1.6525 Calculate the square root of the right side: 1.285496013 Break this problem into two subproblems by setting (x + -0.55) equal to 1.285496013 and -1.285496013.Subproblem 1
x + -0.55 = 1.285496013 Simplifying x + -0.55 = 1.285496013 Reorder the terms: -0.55 + x = 1.285496013 Solving -0.55 + x = 1.285496013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.285496013 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.285496013 + 0.55 x = 1.285496013 + 0.55 Combine like terms: 1.285496013 + 0.55 = 1.835496013 x = 1.835496013 Simplifying x = 1.835496013Subproblem 2
x + -0.55 = -1.285496013 Simplifying x + -0.55 = -1.285496013 Reorder the terms: -0.55 + x = -1.285496013 Solving -0.55 + x = -1.285496013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.285496013 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.285496013 + 0.55 x = -1.285496013 + 0.55 Combine like terms: -1.285496013 + 0.55 = -0.735496013 x = -0.735496013 Simplifying x = -0.735496013Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.835496013, -0.735496013}
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