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Simplifying x4 + -8x2 + 10 = 0 Reorder the terms: 10 + -8x2 + x4 = 0 Solving 10 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8x2 + -10 + x4 = 0 + -10 Reorder the terms: 10 + -10 + -8x2 + x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8x2 + x4 = 0 + -10 -8x2 + x4 = 0 + -10 Combine like terms: 0 + -10 = -10 -8x2 + x4 = -10 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -10 + 16 Reorder the terms: 16 + -8x2 + x4 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -4 = 2.449489743 Simplifying x2 + -4 = 2.449489743 Reorder the terms: -4 + x2 = 2.449489743 Solving -4 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 2.449489743 + 4 x2 = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 x2 = 6.449489743 Simplifying x2 = 6.449489743 Take the square root of each side: x = {-2.539584561, 2.539584561}Subproblem 2
x2 + -4 = -2.449489743 Simplifying x2 + -4 = -2.449489743 Reorder the terms: -4 + x2 = -2.449489743 Solving -4 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -2.449489743 + 4 x2 = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 x2 = 1.550510257 Simplifying x2 = 1.550510257 Take the square root of each side: x = {-1.245194867, 1.245194867}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.539584561, 2.539584561, -1.245194867, 1.245194867}
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