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Simplifying 18x2 + 5x + -25 = 0 Reorder the terms: -25 + 5x + 18x2 = 0 Solving -25 + 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'. -1.388888889 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '1.388888889' to each side of the equation. -1.388888889 + 0.2777777778x + 1.388888889 + x2 = 0 + 1.388888889 Reorder the terms: -1.388888889 + 1.388888889 + 0.2777777778x + x2 = 0 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + 0.2777777778x + x2 = 0 + 1.388888889 0.2777777778x + x2 = 0 + 1.388888889 Combine like terms: 0 + 1.388888889 = 1.388888889 0.2777777778x + x2 = 1.388888889 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 = 1.388888889 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = 1.388888889 + 0.01929012346 Combine like terms: 1.388888889 + 0.01929012346 = 1.40817901246 0.01929012346 + 0.2777777778x + x2 = 1.40817901246 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = 1.40817901246 Calculate the square root of the right side: 1.186667187 Break this problem into two subproblems by setting (x + 0.1388888889) equal to 1.186667187 and -1.186667187.Subproblem 1
x + 0.1388888889 = 1.186667187 Simplifying x + 0.1388888889 = 1.186667187 Reorder the terms: 0.1388888889 + x = 1.186667187 Solving 0.1388888889 + x = 1.186667187 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 = 1.186667187 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = 1.186667187 + -0.1388888889 x = 1.186667187 + -0.1388888889 Combine like terms: 1.186667187 + -0.1388888889 = 1.0477782981 x = 1.0477782981 Simplifying x = 1.0477782981Subproblem 2
x + 0.1388888889 = -1.186667187 Simplifying x + 0.1388888889 = -1.186667187 Reorder the terms: 0.1388888889 + x = -1.186667187 Solving 0.1388888889 + x = -1.186667187 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 = -1.186667187 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = -1.186667187 + -0.1388888889 x = -1.186667187 + -0.1388888889 Combine like terms: -1.186667187 + -0.1388888889 = -1.3255560759 x = -1.3255560759 Simplifying x = -1.3255560759Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0477782981, -1.3255560759}
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