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Simplifying b4 + -26b2 + -256 = 0 Reorder the terms: -256 + -26b2 + b4 = 0 Solving -256 + -26b2 + b4 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + -26b2 + 256 + b4 = 0 + 256 Reorder the terms: -256 + 256 + -26b2 + b4 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -26b2 + b4 = 0 + 256 -26b2 + b4 = 0 + 256 Combine like terms: 0 + 256 = 256 -26b2 + b4 = 256 The b term is -26b2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26b2 + 169 + b4 = 256 + 169 Reorder the terms: 169 + -26b2 + b4 = 256 + 169 Combine like terms: 256 + 169 = 425 169 + -26b2 + b4 = 425 Factor a perfect square on the left side: (b2 + -13)(b2 + -13) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (b2 + -13) equal to 20.615528128 and -20.615528128.Subproblem 1
b2 + -13 = 20.615528128 Simplifying b2 + -13 = 20.615528128 Reorder the terms: -13 + b2 = 20.615528128 Solving -13 + b2 = 20.615528128 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + b2 = 20.615528128 + 13 Combine like terms: -13 + 13 = 0 0 + b2 = 20.615528128 + 13 b2 = 20.615528128 + 13 Combine like terms: 20.615528128 + 13 = 33.615528128 b2 = 33.615528128 Simplifying b2 = 33.615528128 Take the square root of each side: b = {-5.797889972, 5.797889972}Subproblem 2
b2 + -13 = -20.615528128 Simplifying b2 + -13 = -20.615528128 Reorder the terms: -13 + b2 = -20.615528128 Solving -13 + b2 = -20.615528128 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + b2 = -20.615528128 + 13 Combine like terms: -13 + 13 = 0 0 + b2 = -20.615528128 + 13 b2 = -20.615528128 + 13 Combine like terms: -20.615528128 + 13 = -7.615528128 b2 = -7.615528128 Simplifying b2 = -7.615528128 Reorder the terms: 7.615528128 + b2 = -7.615528128 + 7.615528128 Combine like terms: -7.615528128 + 7.615528128 = 0.000000000 7.615528128 + 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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