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Simplifying -18x2 + 5x + 118 = 0 Reorder the terms: 118 + 5x + -18x2 = 0 Solving 118 + 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'. -6.555555556 + -0.2777777778x + x2 = 0 Move the constant term to the right: Add '6.555555556' to each side of the equation. -6.555555556 + -0.2777777778x + 6.555555556 + x2 = 0 + 6.555555556 Reorder the terms: -6.555555556 + 6.555555556 + -0.2777777778x + x2 = 0 + 6.555555556 Combine like terms: -6.555555556 + 6.555555556 = 0.000000000 0.000000000 + -0.2777777778x + x2 = 0 + 6.555555556 -0.2777777778x + x2 = 0 + 6.555555556 Combine like terms: 0 + 6.555555556 = 6.555555556 -0.2777777778x + x2 = 6.555555556 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 = 6.555555556 + 0.01929012346 Reorder the terms: 0.01929012346 + -0.2777777778x + x2 = 6.555555556 + 0.01929012346 Combine like terms: 6.555555556 + 0.01929012346 = 6.57484567946 0.01929012346 + -0.2777777778x + x2 = 6.57484567946 Factor a perfect square on the left side: (x + -0.1388888889)(x + -0.1388888889) = 6.57484567946 Calculate the square root of the right side: 2.564146189 Break this problem into two subproblems by setting (x + -0.1388888889) equal to 2.564146189 and -2.564146189.Subproblem 1
x + -0.1388888889 = 2.564146189 Simplifying x + -0.1388888889 = 2.564146189 Reorder the terms: -0.1388888889 + x = 2.564146189 Solving -0.1388888889 + x = 2.564146189 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 = 2.564146189 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = 2.564146189 + 0.1388888889 x = 2.564146189 + 0.1388888889 Combine like terms: 2.564146189 + 0.1388888889 = 2.7030350779 x = 2.7030350779 Simplifying x = 2.7030350779Subproblem 2
x + -0.1388888889 = -2.564146189 Simplifying x + -0.1388888889 = -2.564146189 Reorder the terms: -0.1388888889 + x = -2.564146189 Solving -0.1388888889 + x = -2.564146189 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 = -2.564146189 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = -2.564146189 + 0.1388888889 x = -2.564146189 + 0.1388888889 Combine like terms: -2.564146189 + 0.1388888889 = -2.4252573001 x = -2.4252573001 Simplifying x = -2.4252573001Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7030350779, -2.4252573001}
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