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Simplifying 2b2 + 2b + -20 = 0 Reorder the terms: -20 + 2b + 2b2 = 0 Solving -20 + 2b + 2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + b + b2)' equal to zero and attempt to solve: Simplifying -10 + b + b2 = 0 Solving -10 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + b + b2 = 0 + 10 b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 b + b2 = 10 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. b + 0.25 + b2 = 10 + 0.25 Reorder the terms: 0.25 + b + b2 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + b + b2 = 10.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (b + 0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
b + 0.5 = 3.201562119 Simplifying b + 0.5 = 3.201562119 Reorder the terms: 0.5 + b = 3.201562119 Solving 0.5 + b = 3.201562119 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 3.201562119 + -0.5 b = 3.201562119 + -0.5 Combine like terms: 3.201562119 + -0.5 = 2.701562119 b = 2.701562119 Simplifying b = 2.701562119Subproblem 2
b + 0.5 = -3.201562119 Simplifying b + 0.5 = -3.201562119 Reorder the terms: 0.5 + b = -3.201562119 Solving 0.5 + b = -3.201562119 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -3.201562119 + -0.5 b = -3.201562119 + -0.5 Combine like terms: -3.201562119 + -0.5 = -3.701562119 b = -3.701562119 Simplifying b = -3.701562119Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.701562119, -3.701562119}Solution
b = {2.701562119, -3.701562119}
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