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Simplifying 6b2 + -40 = -8b + 2b2 Reorder the terms: -40 + 6b2 = -8b + 2b2 Solving -40 + 6b2 = -8b + 2b2 Solving for variable 'b'. Reorder the terms: -40 + 8b + 6b2 + -2b2 = -8b + 2b2 + 8b + -2b2 Combine like terms: 6b2 + -2b2 = 4b2 -40 + 8b + 4b2 = -8b + 2b2 + 8b + -2b2 Reorder the terms: -40 + 8b + 4b2 = -8b + 8b + 2b2 + -2b2 Combine like terms: -8b + 8b = 0 -40 + 8b + 4b2 = 0 + 2b2 + -2b2 -40 + 8b + 4b2 = 2b2 + -2b2 Combine like terms: 2b2 + -2b2 = 0 -40 + 8b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 2b + b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + 2b + b2)' equal to zero and attempt to solve: Simplifying -10 + 2b + b2 = 0 Solving -10 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + 2b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2b + b2 = 0 + 10 2b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 2b + b2 = 10 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 10 + 1 Reorder the terms: 1 + 2b + b2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2b + b2 = 11 Factor a perfect square on the left side: (b + 1)(b + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
b + 1 = 3.31662479 Simplifying b + 1 = 3.31662479 Reorder the terms: 1 + b = 3.31662479 Solving 1 + b = 3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + b = 3.31662479 + -1 b = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 b = 2.31662479 Simplifying b = 2.31662479Subproblem 2
b + 1 = -3.31662479 Simplifying b + 1 = -3.31662479 Reorder the terms: 1 + b = -3.31662479 Solving 1 + b = -3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + b = -3.31662479 + -1 b = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 b = -4.31662479 Simplifying b = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.31662479, -4.31662479}Solution
b = {2.31662479, -4.31662479}
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