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Simplifying 36x2 + -1x = 12 Reorder the terms: -1x + 36x2 = 12 Solving -1x + 36x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -1x + 36x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -1x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3333333333 + -0.02777777778x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.02777777778x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.02777777778x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.02777777778x + x2 = 0 + 0.3333333333 -0.02777777778x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.02777777778x + x2 = 0.3333333333 The x term is -0.02777777778x. Take half its coefficient (-0.01388888889). Square it (0.0001929012346) and add it to both sides. Add '0.0001929012346' to each side of the equation. -0.02777777778x + 0.0001929012346 + x2 = 0.3333333333 + 0.0001929012346 Reorder the terms: 0.0001929012346 + -0.02777777778x + x2 = 0.3333333333 + 0.0001929012346 Combine like terms: 0.3333333333 + 0.0001929012346 = 0.3335262345346 0.0001929012346 + -0.02777777778x + x2 = 0.3335262345346 Factor a perfect square on the left side: (x + -0.01388888889)(x + -0.01388888889) = 0.3335262345346 Calculate the square root of the right side: 0.577517302 Break this problem into two subproblems by setting (x + -0.01388888889) equal to 0.577517302 and -0.577517302.Subproblem 1
x + -0.01388888889 = 0.577517302 Simplifying x + -0.01388888889 = 0.577517302 Reorder the terms: -0.01388888889 + x = 0.577517302 Solving -0.01388888889 + x = 0.577517302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01388888889' to each side of the equation. -0.01388888889 + 0.01388888889 + x = 0.577517302 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = 0.577517302 + 0.01388888889 x = 0.577517302 + 0.01388888889 Combine like terms: 0.577517302 + 0.01388888889 = 0.59140619089 x = 0.59140619089 Simplifying x = 0.59140619089Subproblem 2
x + -0.01388888889 = -0.577517302 Simplifying x + -0.01388888889 = -0.577517302 Reorder the terms: -0.01388888889 + x = -0.577517302 Solving -0.01388888889 + x = -0.577517302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01388888889' to each side of the equation. -0.01388888889 + 0.01388888889 + x = -0.577517302 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = -0.577517302 + 0.01388888889 x = -0.577517302 + 0.01388888889 Combine like terms: -0.577517302 + 0.01388888889 = -0.56362841311 x = -0.56362841311 Simplifying x = -0.56362841311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.59140619089, -0.56362841311}
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