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Simplifying b4 + -7b2 + 3 = 0 Reorder the terms: 3 + -7b2 + b4 = 0 Solving 3 + -7b2 + b4 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -7b2 + -3 + b4 = 0 + -3 Reorder the terms: 3 + -3 + -7b2 + b4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7b2 + b4 = 0 + -3 -7b2 + b4 = 0 + -3 Combine like terms: 0 + -3 = -3 -7b2 + b4 = -3 The b term is -7b2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7b2 + 12.25 + b4 = -3 + 12.25 Reorder the terms: 12.25 + -7b2 + b4 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + -7b2 + b4 = 9.25 Factor a perfect square on the left side: (b2 + -3.5)(b2 + -3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (b2 + -3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
b2 + -3.5 = 3.041381265 Simplifying b2 + -3.5 = 3.041381265 Reorder the terms: -3.5 + b2 = 3.041381265 Solving -3.5 + b2 = 3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b2 = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b2 = 3.041381265 + 3.5 b2 = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 b2 = 6.541381265 Simplifying b2 = 6.541381265 Take the square root of each side: b = {-2.557612415, 2.557612415}Subproblem 2
b2 + -3.5 = -3.041381265 Simplifying b2 + -3.5 = -3.041381265 Reorder the terms: -3.5 + b2 = -3.041381265 Solving -3.5 + b2 = -3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b2 = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b2 = -3.041381265 + 3.5 b2 = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 b2 = 0.458618735 Simplifying b2 = 0.458618735 Take the square root of each side: b = {-0.677213951, 0.677213951}Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.557612415, 2.557612415, -0.677213951, 0.677213951}
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