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Simplifying 18x4 + -5x2 + -4 = 0 Reorder the terms: -4 + -5x2 + 18x4 = 0 Solving -4 + -5x2 + 18x4 = 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'. -0.2222222222 + -0.2777777778x2 + x4 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.2777777778x2 + 0.2222222222 + x4 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.2777777778x2 + x4 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.2777777778x2 + x4 = 0 + 0.2222222222 -0.2777777778x2 + x4 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.2777777778x2 + x4 = 0.2222222222 The x term is -0.2777777778x2. 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. -0.2777777778x2 + 0.01929012346 + x4 = 0.2222222222 + 0.01929012346 Reorder the terms: 0.01929012346 + -0.2777777778x2 + x4 = 0.2222222222 + 0.01929012346 Combine like terms: 0.2222222222 + 0.01929012346 = 0.24151234566 0.01929012346 + -0.2777777778x2 + x4 = 0.24151234566 Factor a perfect square on the left side: (x2 + -0.1388888889)(x2 + -0.1388888889) = 0.24151234566 Calculate the square root of the right side: 0.491439056 Break this problem into two subproblems by setting (x2 + -0.1388888889) equal to 0.491439056 and -0.491439056.Subproblem 1
x2 + -0.1388888889 = 0.491439056 Simplifying x2 + -0.1388888889 = 0.491439056 Reorder the terms: -0.1388888889 + x2 = 0.491439056 Solving -0.1388888889 + x2 = 0.491439056 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 + x2 = 0.491439056 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x2 = 0.491439056 + 0.1388888889 x2 = 0.491439056 + 0.1388888889 Combine like terms: 0.491439056 + 0.1388888889 = 0.6303279449 x2 = 0.6303279449 Simplifying x2 = 0.6303279449 Take the square root of each side: x = {-0.793931952, 0.793931952}Subproblem 2
x2 + -0.1388888889 = -0.491439056 Simplifying x2 + -0.1388888889 = -0.491439056 Reorder the terms: -0.1388888889 + x2 = -0.491439056 Solving -0.1388888889 + x2 = -0.491439056 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 + x2 = -0.491439056 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x2 = -0.491439056 + 0.1388888889 x2 = -0.491439056 + 0.1388888889 Combine like terms: -0.491439056 + 0.1388888889 = -0.3525501671 x2 = -0.3525501671 Simplifying x2 = -0.3525501671 Reorder the terms: 0.3525501671 + x2 = -0.3525501671 + 0.3525501671 Combine like terms: -0.3525501671 + 0.3525501671 = 0.0000000000 0.3525501671 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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