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Simplifying 18x2 + -5x + -35 = 0 Reorder the terms: -35 + -5x + 18x2 = 0 Solving -35 + -5x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.944444444 + -0.2777777778x + x2 = 0 Move the constant term to the right: Add '1.944444444' to each side of the equation. -1.944444444 + -0.2777777778x + 1.944444444 + x2 = 0 + 1.944444444 Reorder the terms: -1.944444444 + 1.944444444 + -0.2777777778x + x2 = 0 + 1.944444444 Combine like terms: -1.944444444 + 1.944444444 = 0.000000000 0.000000000 + -0.2777777778x + x2 = 0 + 1.944444444 -0.2777777778x + x2 = 0 + 1.944444444 Combine like terms: 0 + 1.944444444 = 1.944444444 -0.2777777778x + x2 = 1.944444444 The x term is -0.2777777778x. Take half its coefficient (-0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. -0.2777777778x + 0.01929012346 + x2 = 1.944444444 + 0.01929012346 Reorder the terms: 0.01929012346 + -0.2777777778x + x2 = 1.944444444 + 0.01929012346 Combine like terms: 1.944444444 + 0.01929012346 = 1.96373456746 0.01929012346 + -0.2777777778x + x2 = 1.96373456746 Factor a perfect square on the left side: (x + -0.1388888889)(x + -0.1388888889) = 1.96373456746 Calculate the square root of the right side: 1.401333139 Break this problem into two subproblems by setting (x + -0.1388888889) equal to 1.401333139 and -1.401333139.Subproblem 1
x + -0.1388888889 = 1.401333139 Simplifying x + -0.1388888889 = 1.401333139 Reorder the terms: -0.1388888889 + x = 1.401333139 Solving -0.1388888889 + x = 1.401333139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1388888889' to each side of the equation. -0.1388888889 + 0.1388888889 + x = 1.401333139 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = 1.401333139 + 0.1388888889 x = 1.401333139 + 0.1388888889 Combine like terms: 1.401333139 + 0.1388888889 = 1.5402220279 x = 1.5402220279 Simplifying x = 1.5402220279Subproblem 2
x + -0.1388888889 = -1.401333139 Simplifying x + -0.1388888889 = -1.401333139 Reorder the terms: -0.1388888889 + x = -1.401333139 Solving -0.1388888889 + x = -1.401333139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1388888889' to each side of the equation. -0.1388888889 + 0.1388888889 + x = -1.401333139 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = -1.401333139 + 0.1388888889 x = -1.401333139 + 0.1388888889 Combine like terms: -1.401333139 + 0.1388888889 = -1.2624442501 x = -1.2624442501 Simplifying x = -1.2624442501Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5402220279, -1.2624442501}
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