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Simplifying x4 + -16x2 + 24 = 0 Reorder the terms: 24 + -16x2 + x4 = 0 Solving 24 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -16x2 + -24 + x4 = 0 + -24 Reorder the terms: 24 + -24 + -16x2 + x4 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -16x2 + x4 = 0 + -24 -16x2 + x4 = 0 + -24 Combine like terms: 0 + -24 = -24 -16x2 + x4 = -24 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -24 + 64 Reorder the terms: 64 + -16x2 + x4 = -24 + 64 Combine like terms: -24 + 64 = 40 64 + -16x2 + x4 = 40 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x2 + -8) equal to 6.32455532 and -6.32455532.Subproblem 1
x2 + -8 = 6.32455532 Simplifying x2 + -8 = 6.32455532 Reorder the terms: -8 + x2 = 6.32455532 Solving -8 + x2 = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 6.32455532 + 8 x2 = 6.32455532 + 8 Combine like terms: 6.32455532 + 8 = 14.32455532 x2 = 14.32455532 Simplifying x2 = 14.32455532 Take the square root of each side: x = {-3.784779428, 3.784779428}Subproblem 2
x2 + -8 = -6.32455532 Simplifying x2 + -8 = -6.32455532 Reorder the terms: -8 + x2 = -6.32455532 Solving -8 + x2 = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -6.32455532 + 8 x2 = -6.32455532 + 8 Combine like terms: -6.32455532 + 8 = 1.67544468 x2 = 1.67544468 Simplifying x2 = 1.67544468 Take the square root of each side: x = {-1.294389694, 1.294389694}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.784779428, 3.784779428, -1.294389694, 1.294389694}
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