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Simplifying b4 + 17b2 + -4 = 0 Reorder the terms: -4 + 17b2 + b4 = 0 Solving -4 + 17b2 + b4 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 17b2 + 4 + b4 = 0 + 4 Reorder the terms: -4 + 4 + 17b2 + b4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 17b2 + b4 = 0 + 4 17b2 + b4 = 0 + 4 Combine like terms: 0 + 4 = 4 17b2 + b4 = 4 The b term is 17b2. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17b2 + 72.25 + b4 = 4 + 72.25 Reorder the terms: 72.25 + 17b2 + b4 = 4 + 72.25 Combine like terms: 4 + 72.25 = 76.25 72.25 + 17b2 + b4 = 76.25 Factor a perfect square on the left side: (b2 + 8.5)(b2 + 8.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (b2 + 8.5) equal to 8.732124598 and -8.732124598.Subproblem 1
b2 + 8.5 = 8.732124598 Simplifying b2 + 8.5 = 8.732124598 Reorder the terms: 8.5 + b2 = 8.732124598 Solving 8.5 + b2 = 8.732124598 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + b2 = 8.732124598 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + b2 = 8.732124598 + -8.5 b2 = 8.732124598 + -8.5 Combine like terms: 8.732124598 + -8.5 = 0.232124598 b2 = 0.232124598 Simplifying b2 = 0.232124598 Take the square root of each side: b = {-0.481793107, 0.481793107}Subproblem 2
b2 + 8.5 = -8.732124598 Simplifying b2 + 8.5 = -8.732124598 Reorder the terms: 8.5 + b2 = -8.732124598 Solving 8.5 + b2 = -8.732124598 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + b2 = -8.732124598 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + b2 = -8.732124598 + -8.5 b2 = -8.732124598 + -8.5 Combine like terms: -8.732124598 + -8.5 = -17.232124598 b2 = -17.232124598 Simplifying b2 = -17.232124598 Reorder the terms: 17.232124598 + b2 = -17.232124598 + 17.232124598 Combine like terms: -17.232124598 + 17.232124598 = 0.000000000 17.232124598 + 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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