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Simplifying 5x4 + -180x2 + 1296 = 0 Reorder the terms: 1296 + -180x2 + 5x4 = 0 Solving 1296 + -180x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 259.2 + -36x2 + x4 = 0 Move the constant term to the right: Add '-259.2' to each side of the equation. 259.2 + -36x2 + -259.2 + x4 = 0 + -259.2 Reorder the terms: 259.2 + -259.2 + -36x2 + x4 = 0 + -259.2 Combine like terms: 259.2 + -259.2 = 0.0 0.0 + -36x2 + x4 = 0 + -259.2 -36x2 + x4 = 0 + -259.2 Combine like terms: 0 + -259.2 = -259.2 -36x2 + x4 = -259.2 The x term is -36x2. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x2 + 324 + x4 = -259.2 + 324 Reorder the terms: 324 + -36x2 + x4 = -259.2 + 324 Combine like terms: -259.2 + 324 = 64.8 324 + -36x2 + x4 = 64.8 Factor a perfect square on the left side: (x2 + -18)(x2 + -18) = 64.8 Calculate the square root of the right side: 8.049844719 Break this problem into two subproblems by setting (x2 + -18) equal to 8.049844719 and -8.049844719.Subproblem 1
x2 + -18 = 8.049844719 Simplifying x2 + -18 = 8.049844719 Reorder the terms: -18 + x2 = 8.049844719 Solving -18 + x2 = 8.049844719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x2 = 8.049844719 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = 8.049844719 + 18 x2 = 8.049844719 + 18 Combine like terms: 8.049844719 + 18 = 26.049844719 x2 = 26.049844719 Simplifying x2 = 26.049844719 Take the square root of each side: x = {-5.10390485, 5.10390485}Subproblem 2
x2 + -18 = -8.049844719 Simplifying x2 + -18 = -8.049844719 Reorder the terms: -18 + x2 = -8.049844719 Solving -18 + x2 = -8.049844719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x2 = -8.049844719 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = -8.049844719 + 18 x2 = -8.049844719 + 18 Combine like terms: -8.049844719 + 18 = 9.950155281 x2 = 9.950155281 Simplifying x2 = 9.950155281 Take the square root of each side: x = {-3.154386673, 3.154386673}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.10390485, 5.10390485, -3.154386673, 3.154386673}
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