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Simplifying 2b2 + 14b + -30 = 0 Reorder the terms: -30 + 14b + 2b2 = 0 Solving -30 + 14b + 2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 7b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 7b + b2)' equal to zero and attempt to solve: Simplifying -15 + 7b + b2 = 0 Solving -15 + 7b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 7b + 15 + b2 = 0 + 15 Reorder the terms: -15 + 15 + 7b + b2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7b + b2 = 0 + 15 7b + b2 = 0 + 15 Combine like terms: 0 + 15 = 15 7b + b2 = 15 The b term is 7b. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7b + 12.25 + b2 = 15 + 12.25 Reorder the terms: 12.25 + 7b + b2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7b + b2 = 27.25 Factor a perfect square on the left side: (b + 3.5)(b + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (b + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
b + 3.5 = 5.220153254 Simplifying b + 3.5 = 5.220153254 Reorder the terms: 3.5 + b = 5.220153254 Solving 3.5 + b = 5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = 5.220153254 + -3.5 b = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 b = 1.720153254 Simplifying b = 1.720153254Subproblem 2
b + 3.5 = -5.220153254 Simplifying b + 3.5 = -5.220153254 Reorder the terms: 3.5 + b = -5.220153254 Solving 3.5 + b = -5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = -5.220153254 + -3.5 b = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 b = -8.720153254 Simplifying b = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.720153254, -8.720153254}Solution
b = {1.720153254, -8.720153254}
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