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Simplifying x4 + -12x2 + 2 = 0 Reorder the terms: 2 + -12x2 + x4 = 0 Solving 2 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -12x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -12x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -12x2 + x4 = 0 + -2 -12x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -12x2 + x4 = -2 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = -2 + 36 Reorder the terms: 36 + -12x2 + x4 = -2 + 36 Combine like terms: -2 + 36 = 34 36 + -12x2 + x4 = 34 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x2 + -6) equal to 5.830951895 and -5.830951895.Subproblem 1
x2 + -6 = 5.830951895 Simplifying x2 + -6 = 5.830951895 Reorder the terms: -6 + x2 = 5.830951895 Solving -6 + x2 = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 5.830951895 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 5.830951895 + 6 x2 = 5.830951895 + 6 Combine like terms: 5.830951895 + 6 = 11.830951895 x2 = 11.830951895 Simplifying x2 = 11.830951895 Take the square root of each side: x = {-3.439615079, 3.439615079}Subproblem 2
x2 + -6 = -5.830951895 Simplifying x2 + -6 = -5.830951895 Reorder the terms: -6 + x2 = -5.830951895 Solving -6 + x2 = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -5.830951895 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -5.830951895 + 6 x2 = -5.830951895 + 6 Combine like terms: -5.830951895 + 6 = 0.169048105 x2 = 0.169048105 Simplifying x2 = 0.169048105 Take the square root of each side: x = {-0.4111546, 0.4111546}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.439615079, 3.439615079, -0.4111546, 0.4111546}
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