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Simplifying 9x4 + 31x2 + -180 = 0 Reorder the terms: -180 + 31x2 + 9x4 = 0 Solving -180 + 31x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -20 + 3.444444444x2 + x4 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 3.444444444x2 + 20 + x4 = 0 + 20 Reorder the terms: -20 + 20 + 3.444444444x2 + x4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3.444444444x2 + x4 = 0 + 20 3.444444444x2 + x4 = 0 + 20 Combine like terms: 0 + 20 = 20 3.444444444x2 + x4 = 20 The x term is 3.444444444x2. Take half its coefficient (1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. 3.444444444x2 + 2.966049382 + x4 = 20 + 2.966049382 Reorder the terms: 2.966049382 + 3.444444444x2 + x4 = 20 + 2.966049382 Combine like terms: 20 + 2.966049382 = 22.966049382 2.966049382 + 3.444444444x2 + x4 = 22.966049382 Factor a perfect square on the left side: (x2 + 1.722222222)(x2 + 1.722222222) = 22.966049382 Calculate the square root of the right side: 4.79229062 Break this problem into two subproblems by setting (x2 + 1.722222222) equal to 4.79229062 and -4.79229062.Subproblem 1
x2 + 1.722222222 = 4.79229062 Simplifying x2 + 1.722222222 = 4.79229062 Reorder the terms: 1.722222222 + x2 = 4.79229062 Solving 1.722222222 + x2 = 4.79229062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.722222222' to each side of the equation. 1.722222222 + -1.722222222 + x2 = 4.79229062 + -1.722222222 Combine like terms: 1.722222222 + -1.722222222 = 0.000000000 0.000000000 + x2 = 4.79229062 + -1.722222222 x2 = 4.79229062 + -1.722222222 Combine like terms: 4.79229062 + -1.722222222 = 3.070068398 x2 = 3.070068398 Simplifying x2 = 3.070068398 Take the square root of each side: x = {-1.752161065, 1.752161065}Subproblem 2
x2 + 1.722222222 = -4.79229062 Simplifying x2 + 1.722222222 = -4.79229062 Reorder the terms: 1.722222222 + x2 = -4.79229062 Solving 1.722222222 + x2 = -4.79229062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.722222222' to each side of the equation. 1.722222222 + -1.722222222 + x2 = -4.79229062 + -1.722222222 Combine like terms: 1.722222222 + -1.722222222 = 0.000000000 0.000000000 + x2 = -4.79229062 + -1.722222222 x2 = -4.79229062 + -1.722222222 Combine like terms: -4.79229062 + -1.722222222 = -6.514512842 x2 = -6.514512842 Simplifying x2 = -6.514512842 Reorder the terms: 6.514512842 + x2 = -6.514512842 + 6.514512842 Combine like terms: -6.514512842 + 6.514512842 = 0.000000000 6.514512842 + x2 = 0.000000000 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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