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Simplifying 121x2 + -132x + -27 = 0 Reorder the terms: -27 + -132x + 121x2 = 0 Solving -27 + -132x + 121x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -0.2231404959 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '0.2231404959' to each side of the equation. -0.2231404959 + -1.090909091x + 0.2231404959 + x2 = 0 + 0.2231404959 Reorder the terms: -0.2231404959 + 0.2231404959 + -1.090909091x + x2 = 0 + 0.2231404959 Combine like terms: -0.2231404959 + 0.2231404959 = 0.0000000000 0.0000000000 + -1.090909091x + x2 = 0 + 0.2231404959 -1.090909091x + x2 = 0 + 0.2231404959 Combine like terms: 0 + 0.2231404959 = 0.2231404959 -1.090909091x + x2 = 0.2231404959 The x term is -1.090909091x. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091x + 0.2975206612 + x2 = 0.2231404959 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 0.2231404959 + 0.2975206612 Combine like terms: 0.2231404959 + 0.2975206612 = 0.5206611571 0.2975206612 + -1.090909091x + x2 = 0.5206611571 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 0.5206611571 Calculate the square root of the right side: 0.721568539 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 0.721568539 and -0.721568539.Subproblem 1
x + -0.5454545455 = 0.721568539 Simplifying x + -0.5454545455 = 0.721568539 Reorder the terms: -0.5454545455 + x = 0.721568539 Solving -0.5454545455 + x = 0.721568539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = 0.721568539 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 0.721568539 + 0.5454545455 x = 0.721568539 + 0.5454545455 Combine like terms: 0.721568539 + 0.5454545455 = 1.2670230845 x = 1.2670230845 Simplifying x = 1.2670230845Subproblem 2
x + -0.5454545455 = -0.721568539 Simplifying x + -0.5454545455 = -0.721568539 Reorder the terms: -0.5454545455 + x = -0.721568539 Solving -0.5454545455 + x = -0.721568539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = -0.721568539 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -0.721568539 + 0.5454545455 x = -0.721568539 + 0.5454545455 Combine like terms: -0.721568539 + 0.5454545455 = -0.1761139935 x = -0.1761139935 Simplifying x = -0.1761139935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2670230845, -0.1761139935}
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