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Simplifying b4 + -22b3 = 10b2 Reorder the terms: -22b3 + b4 = 10b2 Solving -22b3 + b4 = 10b2 Solving for variable 'b'. Reorder the terms: -10b2 + -22b3 + b4 = 10b2 + -10b2 Combine like terms: 10b2 + -10b2 = 0 -10b2 + -22b3 + b4 = 0 Factor out the Greatest Common Factor (GCF), 'b2'. b2(-10 + -22b + b2) = 0Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(-10 + -22b + b2)' equal to zero and attempt to solve: Simplifying -10 + -22b + b2 = 0 Solving -10 + -22b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -22b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + -22b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -22b + b2 = 0 + 10 -22b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 -22b + b2 = 10 The b term is -22b. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22b + 121 + b2 = 10 + 121 Reorder the terms: 121 + -22b + b2 = 10 + 121 Combine like terms: 10 + 121 = 131 121 + -22b + b2 = 131 Factor a perfect square on the left side: (b + -11)(b + -11) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (b + -11) equal to 11.445523142 and -11.445523142.Subproblem 1
b + -11 = 11.445523142 Simplifying b + -11 = 11.445523142 Reorder the terms: -11 + b = 11.445523142 Solving -11 + b = 11.445523142 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + b = 11.445523142 + 11 Combine like terms: -11 + 11 = 0 0 + b = 11.445523142 + 11 b = 11.445523142 + 11 Combine like terms: 11.445523142 + 11 = 22.445523142 b = 22.445523142 Simplifying b = 22.445523142Subproblem 2
b + -11 = -11.445523142 Simplifying b + -11 = -11.445523142 Reorder the terms: -11 + b = -11.445523142 Solving -11 + b = -11.445523142 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + b = -11.445523142 + 11 Combine like terms: -11 + 11 = 0 0 + b = -11.445523142 + 11 b = -11.445523142 + 11 Combine like terms: -11.445523142 + 11 = -0.445523142 b = -0.445523142 Simplifying b = -0.445523142Solution
The solution to the problem is based on the solutions from the subproblems. b = {22.445523142, -0.445523142}Solution
b = {0, 22.445523142, -0.445523142}
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