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Simplifying 3b2 + -3b + -15 = 0 Reorder the terms: -15 + -3b + 3b2 = 0 Solving -15 + -3b + 3b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -1b + b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1b + b2)' equal to zero and attempt to solve: Simplifying -5 + -1b + b2 = 0 Solving -5 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1b + 5 + b2 = 0 + 5 Reorder the terms: -5 + 5 + -1b + b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b + b2 = 0 + 5 -1b + b2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1b + b2 = 5 The b term is -1b. 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. -1b + 0.25 + b2 = 5 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1b + b2 = 5.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (b + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
b + -0.5 = 2.291287847 Simplifying b + -0.5 = 2.291287847 Reorder the terms: -0.5 + b = 2.291287847 Solving -0.5 + b = 2.291287847 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 = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 2.291287847 + 0.5 b = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 b = 2.791287847 Simplifying b = 2.791287847Subproblem 2
b + -0.5 = -2.291287847 Simplifying b + -0.5 = -2.291287847 Reorder the terms: -0.5 + b = -2.291287847 Solving -0.5 + b = -2.291287847 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 = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -2.291287847 + 0.5 b = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 b = -1.791287847 Simplifying b = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.791287847, -1.791287847}Solution
b = {2.791287847, -1.791287847}
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