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Simplifying 135x2 + -24.81x + -6.607 = 0 Reorder the terms: -6.607 + -24.81x + 135x2 = 0 Solving -6.607 + -24.81x + 135x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 135 the coefficient of the squared term: Divide each side by '135'. -0.04894074074 + -0.1837777778x + x2 = 0 Move the constant term to the right: Add '0.04894074074' to each side of the equation. -0.04894074074 + -0.1837777778x + 0.04894074074 + x2 = 0 + 0.04894074074 Reorder the terms: -0.04894074074 + 0.04894074074 + -0.1837777778x + x2 = 0 + 0.04894074074 Combine like terms: -0.04894074074 + 0.04894074074 = 0.00000000000 0.00000000000 + -0.1837777778x + x2 = 0 + 0.04894074074 -0.1837777778x + x2 = 0 + 0.04894074074 Combine like terms: 0 + 0.04894074074 = 0.04894074074 -0.1837777778x + x2 = 0.04894074074 The x term is -0.1837777778x. Take half its coefficient (-0.0918888889). Square it (0.008443567903) and add it to both sides. Add '0.008443567903' to each side of the equation. -0.1837777778x + 0.008443567903 + x2 = 0.04894074074 + 0.008443567903 Reorder the terms: 0.008443567903 + -0.1837777778x + x2 = 0.04894074074 + 0.008443567903 Combine like terms: 0.04894074074 + 0.008443567903 = 0.057384308643 0.008443567903 + -0.1837777778x + x2 = 0.057384308643 Factor a perfect square on the left side: (x + -0.0918888889)(x + -0.0918888889) = 0.057384308643 Calculate the square root of the right side: 0.239550222 Break this problem into two subproblems by setting (x + -0.0918888889) equal to 0.239550222 and -0.239550222.Subproblem 1
x + -0.0918888889 = 0.239550222 Simplifying x + -0.0918888889 = 0.239550222 Reorder the terms: -0.0918888889 + x = 0.239550222 Solving -0.0918888889 + x = 0.239550222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0918888889' to each side of the equation. -0.0918888889 + 0.0918888889 + x = 0.239550222 + 0.0918888889 Combine like terms: -0.0918888889 + 0.0918888889 = 0.0000000000 0.0000000000 + x = 0.239550222 + 0.0918888889 x = 0.239550222 + 0.0918888889 Combine like terms: 0.239550222 + 0.0918888889 = 0.3314391109 x = 0.3314391109 Simplifying x = 0.3314391109Subproblem 2
x + -0.0918888889 = -0.239550222 Simplifying x + -0.0918888889 = -0.239550222 Reorder the terms: -0.0918888889 + x = -0.239550222 Solving -0.0918888889 + x = -0.239550222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0918888889' to each side of the equation. -0.0918888889 + 0.0918888889 + x = -0.239550222 + 0.0918888889 Combine like terms: -0.0918888889 + 0.0918888889 = 0.0000000000 0.0000000000 + x = -0.239550222 + 0.0918888889 x = -0.239550222 + 0.0918888889 Combine like terms: -0.239550222 + 0.0918888889 = -0.1476613331 x = -0.1476613331 Simplifying x = -0.1476613331Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3314391109, -0.1476613331}
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