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Simplifying 2x2 + -27x + -135 = 0 Reorder the terms: -135 + -27x + 2x2 = 0 Solving -135 + -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'. -67.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + -13.5x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + -13.5x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + -13.5x + x2 = 0 + 67.5 -13.5x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 -13.5x + x2 = 67.5 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 = 67.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = 67.5 + 45.5625 Combine like terms: 67.5 + 45.5625 = 113.0625 45.5625 + -13.5x + x2 = 113.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 113.0625 Calculate the square root of the right side: 10.633085159 Break this problem into two subproblems by setting (x + -6.75) equal to 10.633085159 and -10.633085159.Subproblem 1
x + -6.75 = 10.633085159 Simplifying x + -6.75 = 10.633085159 Reorder the terms: -6.75 + x = 10.633085159 Solving -6.75 + x = 10.633085159 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 = 10.633085159 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 10.633085159 + 6.75 x = 10.633085159 + 6.75 Combine like terms: 10.633085159 + 6.75 = 17.383085159 x = 17.383085159 Simplifying x = 17.383085159Subproblem 2
x + -6.75 = -10.633085159 Simplifying x + -6.75 = -10.633085159 Reorder the terms: -6.75 + x = -10.633085159 Solving -6.75 + x = -10.633085159 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 = -10.633085159 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -10.633085159 + 6.75 x = -10.633085159 + 6.75 Combine like terms: -10.633085159 + 6.75 = -3.883085159 x = -3.883085159 Simplifying x = -3.883085159Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.383085159, -3.883085159}
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