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Simplifying 2b + 4b2 + 2b = 16 Reorder the terms: 2b + 2b + 4b2 = 16 Combine like terms: 2b + 2b = 4b 4b + 4b2 = 16 Solving 4b + 4b2 = 16 Solving for variable 'b'. Reorder the terms: -16 + 4b + 4b2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 4b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + b + b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + b + b2)' equal to zero and attempt to solve: Simplifying -4 + b + b2 = 0 Solving -4 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + b + b2 = 0 + 4 b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 b + b2 = 4 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 = 4 + 0.25 Reorder the terms: 0.25 + b + b2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + b + b2 = 4.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (b + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
b + 0.5 = 2.061552813 Simplifying b + 0.5 = 2.061552813 Reorder the terms: 0.5 + b = 2.061552813 Solving 0.5 + b = 2.061552813 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 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 2.061552813 + -0.5 b = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 b = 1.561552813 Simplifying b = 1.561552813Subproblem 2
b + 0.5 = -2.061552813 Simplifying b + 0.5 = -2.061552813 Reorder the terms: 0.5 + b = -2.061552813 Solving 0.5 + b = -2.061552813 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 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -2.061552813 + -0.5 b = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 b = -2.561552813 Simplifying b = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.561552813, -2.561552813}Solution
b = {1.561552813, -2.561552813}
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