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Simplifying x4 + -26x2 + 121 = 0 Reorder the terms: 121 + -26x2 + x4 = 0 Solving 121 + -26x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-121' to each side of the equation. 121 + -26x2 + -121 + x4 = 0 + -121 Reorder the terms: 121 + -121 + -26x2 + x4 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + -26x2 + x4 = 0 + -121 -26x2 + x4 = 0 + -121 Combine like terms: 0 + -121 = -121 -26x2 + x4 = -121 The x term is -26x2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x2 + 169 + x4 = -121 + 169 Reorder the terms: 169 + -26x2 + x4 = -121 + 169 Combine like terms: -121 + 169 = 48 169 + -26x2 + x4 = 48 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + -13) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + -13 = 6.92820323 Simplifying x2 + -13 = 6.92820323 Reorder the terms: -13 + x2 = 6.92820323 Solving -13 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = 6.92820323 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 6.92820323 + 13 x2 = 6.92820323 + 13 Combine like terms: 6.92820323 + 13 = 19.92820323 x2 = 19.92820323 Simplifying x2 = 19.92820323 Take the square root of each side: x = {-4.464101615, 4.464101615}Subproblem 2
x2 + -13 = -6.92820323 Simplifying x2 + -13 = -6.92820323 Reorder the terms: -13 + x2 = -6.92820323 Solving -13 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = -6.92820323 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -6.92820323 + 13 x2 = -6.92820323 + 13 Combine like terms: -6.92820323 + 13 = 6.07179677 x2 = 6.07179677 Simplifying x2 = 6.07179677 Take the square root of each side: x = {-2.464101615, 2.464101615}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.464101615, 4.464101615, -2.464101615, 2.464101615}
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