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Simplifying x4 + -14x2 + 1 = 0 Reorder the terms: 1 + -14x2 + x4 = 0 Solving 1 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -14x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -14x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -14x2 + x4 = 0 + -1 -14x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -14x2 + x4 = -1 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -1 + 49 Reorder the terms: 49 + -14x2 + x4 = -1 + 49 Combine like terms: -1 + 49 = 48 49 + -14x2 + x4 = 48 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + -7) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + -7 = 6.92820323 Simplifying x2 + -7 = 6.92820323 Reorder the terms: -7 + x2 = 6.92820323 Solving -7 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 6.92820323 + 7 x2 = 6.92820323 + 7 Combine like terms: 6.92820323 + 7 = 13.92820323 x2 = 13.92820323 Simplifying x2 = 13.92820323 Take the square root of each side: x = {-3.732050808, 3.732050808}Subproblem 2
x2 + -7 = -6.92820323 Simplifying x2 + -7 = -6.92820323 Reorder the terms: -7 + x2 = -6.92820323 Solving -7 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -6.92820323 + 7 x2 = -6.92820323 + 7 Combine like terms: -6.92820323 + 7 = 0.07179677 x2 = 0.07179677 Simplifying x2 = 0.07179677 Take the square root of each side: x = {-0.267949193, 0.267949193}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.732050808, 3.732050808, -0.267949193, 0.267949193}
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