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Simplifying 20x2 + 240x + -27 = 0 Reorder the terms: -27 + 240x + 20x2 = 0 Solving -27 + 240x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.35 + 12x + x2 = 0 Move the constant term to the right: Add '1.35' to each side of the equation. -1.35 + 12x + 1.35 + x2 = 0 + 1.35 Reorder the terms: -1.35 + 1.35 + 12x + x2 = 0 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + 12x + x2 = 0 + 1.35 12x + x2 = 0 + 1.35 Combine like terms: 0 + 1.35 = 1.35 12x + x2 = 1.35 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 1.35 + 36 Reorder the terms: 36 + 12x + x2 = 1.35 + 36 Combine like terms: 1.35 + 36 = 37.35 36 + 12x + x2 = 37.35 Factor a perfect square on the left side: (x + 6)(x + 6) = 37.35 Calculate the square root of the right side: 6.111464636 Break this problem into two subproblems by setting (x + 6) equal to 6.111464636 and -6.111464636.Subproblem 1
x + 6 = 6.111464636 Simplifying x + 6 = 6.111464636 Reorder the terms: 6 + x = 6.111464636 Solving 6 + x = 6.111464636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.111464636 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.111464636 + -6 x = 6.111464636 + -6 Combine like terms: 6.111464636 + -6 = 0.111464636 x = 0.111464636 Simplifying x = 0.111464636Subproblem 2
x + 6 = -6.111464636 Simplifying x + 6 = -6.111464636 Reorder the terms: 6 + x = -6.111464636 Solving 6 + x = -6.111464636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.111464636 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.111464636 + -6 x = -6.111464636 + -6 Combine like terms: -6.111464636 + -6 = -12.111464636 x = -12.111464636 Simplifying x = -12.111464636Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.111464636, -12.111464636}
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