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Simplifying b4 + -48b2 + 49 = 0 Reorder the terms: 49 + -48b2 + b4 = 0 Solving 49 + -48b2 + b4 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -48b2 + -49 + b4 = 0 + -49 Reorder the terms: 49 + -49 + -48b2 + b4 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -48b2 + b4 = 0 + -49 -48b2 + b4 = 0 + -49 Combine like terms: 0 + -49 = -49 -48b2 + b4 = -49 The b term is -48b2. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48b2 + 576 + b4 = -49 + 576 Reorder the terms: 576 + -48b2 + b4 = -49 + 576 Combine like terms: -49 + 576 = 527 576 + -48b2 + b4 = 527 Factor a perfect square on the left side: (b2 + -24)(b2 + -24) = 527 Calculate the square root of the right side: 22.956480566 Break this problem into two subproblems by setting (b2 + -24) equal to 22.956480566 and -22.956480566.Subproblem 1
b2 + -24 = 22.956480566 Simplifying b2 + -24 = 22.956480566 Reorder the terms: -24 + b2 = 22.956480566 Solving -24 + b2 = 22.956480566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + b2 = 22.956480566 + 24 Combine like terms: -24 + 24 = 0 0 + b2 = 22.956480566 + 24 b2 = 22.956480566 + 24 Combine like terms: 22.956480566 + 24 = 46.956480566 b2 = 46.956480566 Simplifying b2 = 46.956480566 Take the square root of each side: b = {-6.852479884, 6.852479884}Subproblem 2
b2 + -24 = -22.956480566 Simplifying b2 + -24 = -22.956480566 Reorder the terms: -24 + b2 = -22.956480566 Solving -24 + b2 = -22.956480566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + b2 = -22.956480566 + 24 Combine like terms: -24 + 24 = 0 0 + b2 = -22.956480566 + 24 b2 = -22.956480566 + 24 Combine like terms: -22.956480566 + 24 = 1.043519434 b2 = 1.043519434 Simplifying b2 = 1.043519434 Take the square root of each side: b = {-1.02152799, 1.02152799}Solution
The solution to the problem is based on the solutions from the subproblems. b = {-6.852479884, 6.852479884, -1.02152799, 1.02152799}
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