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Simplifying 27x2 + -27x + -35 = 0 Reorder the terms: -35 + -27x + 27x2 = 0 Solving -35 + -27x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -1.296296296 + -1x + x2 = 0 Move the constant term to the right: Add '1.296296296' to each side of the equation. -1.296296296 + -1x + 1.296296296 + x2 = 0 + 1.296296296 Reorder the terms: -1.296296296 + 1.296296296 + -1x + x2 = 0 + 1.296296296 Combine like terms: -1.296296296 + 1.296296296 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.296296296 -1x + x2 = 0 + 1.296296296 Combine like terms: 0 + 1.296296296 = 1.296296296 -1x + x2 = 1.296296296 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.296296296 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.296296296 + 0.25 Combine like terms: 1.296296296 + 0.25 = 1.546296296 0.25 + -1x + x2 = 1.546296296 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.546296296 Calculate the square root of the right side: 1.243501627 Break this problem into two subproblems by setting (x + -0.5) equal to 1.243501627 and -1.243501627.Subproblem 1
x + -0.5 = 1.243501627 Simplifying x + -0.5 = 1.243501627 Reorder the terms: -0.5 + x = 1.243501627 Solving -0.5 + x = 1.243501627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.243501627 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.243501627 + 0.5 x = 1.243501627 + 0.5 Combine like terms: 1.243501627 + 0.5 = 1.743501627 x = 1.743501627 Simplifying x = 1.743501627Subproblem 2
x + -0.5 = -1.243501627 Simplifying x + -0.5 = -1.243501627 Reorder the terms: -0.5 + x = -1.243501627 Solving -0.5 + x = -1.243501627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.243501627 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.243501627 + 0.5 x = -1.243501627 + 0.5 Combine like terms: -1.243501627 + 0.5 = -0.743501627 x = -0.743501627 Simplifying x = -0.743501627Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.743501627, -0.743501627}
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