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Simplifying 8b4 + 3b2 + 2(b2 + -8) = 0 Reorder the terms: 8b4 + 3b2 + 2(-8 + b2) = 0 8b4 + 3b2 + (-8 * 2 + b2 * 2) = 0 8b4 + 3b2 + (-16 + 2b2) = 0 Reorder the terms: -16 + 3b2 + 2b2 + 8b4 = 0 Combine like terms: 3b2 + 2b2 = 5b2 -16 + 5b2 + 8b4 = 0 Solving -16 + 5b2 + 8b4 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + 0.625b2 + b4 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.625b2 + 2 + b4 = 0 + 2 Reorder the terms: -2 + 2 + 0.625b2 + b4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.625b2 + b4 = 0 + 2 0.625b2 + b4 = 0 + 2 Combine like terms: 0 + 2 = 2 0.625b2 + b4 = 2 The b term is 0.625b2. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625b2 + 0.09765625 + b4 = 2 + 0.09765625 Reorder the terms: 0.09765625 + 0.625b2 + b4 = 2 + 0.09765625 Combine like terms: 2 + 0.09765625 = 2.09765625 0.09765625 + 0.625b2 + b4 = 2.09765625 Factor a perfect square on the left side: (b2 + 0.3125)(b2 + 0.3125) = 2.09765625 Calculate the square root of the right side: 1.448328778 Break this problem into two subproblems by setting (b2 + 0.3125) equal to 1.448328778 and -1.448328778.Subproblem 1
b2 + 0.3125 = 1.448328778 Simplifying b2 + 0.3125 = 1.448328778 Reorder the terms: 0.3125 + b2 = 1.448328778 Solving 0.3125 + b2 = 1.448328778 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + b2 = 1.448328778 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + b2 = 1.448328778 + -0.3125 b2 = 1.448328778 + -0.3125 Combine like terms: 1.448328778 + -0.3125 = 1.135828778 b2 = 1.135828778 Simplifying b2 = 1.135828778 Take the square root of each side: b = {-1.065752681, 1.065752681}Subproblem 2
b2 + 0.3125 = -1.448328778 Simplifying b2 + 0.3125 = -1.448328778 Reorder the terms: 0.3125 + b2 = -1.448328778 Solving 0.3125 + b2 = -1.448328778 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + b2 = -1.448328778 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + b2 = -1.448328778 + -0.3125 b2 = -1.448328778 + -0.3125 Combine like terms: -1.448328778 + -0.3125 = -1.760828778 b2 = -1.760828778 Simplifying b2 = -1.760828778 Reorder the terms: 1.760828778 + b2 = -1.760828778 + 1.760828778 Combine like terms: -1.760828778 + 1.760828778 = 0.000000000 1.760828778 + b2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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