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Simplifying x4 + -26x2 + 81 = 0 Reorder the terms: 81 + -26x2 + x4 = 0 Solving 81 + -26x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -26x2 + -81 + x4 = 0 + -81 Reorder the terms: 81 + -81 + -26x2 + x4 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -26x2 + x4 = 0 + -81 -26x2 + x4 = 0 + -81 Combine like terms: 0 + -81 = -81 -26x2 + x4 = -81 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 = -81 + 169 Reorder the terms: 169 + -26x2 + x4 = -81 + 169 Combine like terms: -81 + 169 = 88 169 + -26x2 + x4 = 88 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x2 + -13) equal to 9.38083152 and -9.38083152.Subproblem 1
x2 + -13 = 9.38083152 Simplifying x2 + -13 = 9.38083152 Reorder the terms: -13 + x2 = 9.38083152 Solving -13 + x2 = 9.38083152 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 = 9.38083152 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 9.38083152 + 13 x2 = 9.38083152 + 13 Combine like terms: 9.38083152 + 13 = 22.38083152 x2 = 22.38083152 Simplifying x2 = 22.38083152 Take the square root of each side: x = {-4.730838353, 4.730838353}Subproblem 2
x2 + -13 = -9.38083152 Simplifying x2 + -13 = -9.38083152 Reorder the terms: -13 + x2 = -9.38083152 Solving -13 + x2 = -9.38083152 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 = -9.38083152 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -9.38083152 + 13 x2 = -9.38083152 + 13 Combine like terms: -9.38083152 + 13 = 3.61916848 x2 = 3.61916848 Simplifying x2 = 3.61916848 Take the square root of each side: x = {-1.902411228, 1.902411228}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.730838353, 4.730838353, -1.902411228, 1.902411228}
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