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Simplifying 3b2 + 36b + 90 = 0 Reorder the terms: 90 + 36b + 3b2 = 0 Solving 90 + 36b + 3b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(30 + 12b + b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(30 + 12b + b2)' equal to zero and attempt to solve: Simplifying 30 + 12b + b2 = 0 Solving 30 + 12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 12b + -30 + b2 = 0 + -30 Reorder the terms: 30 + -30 + 12b + b2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 12b + b2 = 0 + -30 12b + b2 = 0 + -30 Combine like terms: 0 + -30 = -30 12b + b2 = -30 The b term is 12b. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12b + 36 + b2 = -30 + 36 Reorder the terms: 36 + 12b + b2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + 12b + b2 = 6 Factor a perfect square on the left side: (b + 6)(b + 6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + 6) equal to 2.449489743 and -2.449489743.Subproblem 1
b + 6 = 2.449489743 Simplifying b + 6 = 2.449489743 Reorder the terms: 6 + b = 2.449489743 Solving 6 + b = 2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = 2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + b = 2.449489743 + -6 b = 2.449489743 + -6 Combine like terms: 2.449489743 + -6 = -3.550510257 b = -3.550510257 Simplifying b = -3.550510257Subproblem 2
b + 6 = -2.449489743 Simplifying b + 6 = -2.449489743 Reorder the terms: 6 + b = -2.449489743 Solving 6 + b = -2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = -2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + b = -2.449489743 + -6 b = -2.449489743 + -6 Combine like terms: -2.449489743 + -6 = -8.449489743 b = -8.449489743 Simplifying b = -8.449489743Solution
The solution to the problem is based on the solutions from the subproblems. b = {-3.550510257, -8.449489743}Solution
b = {-3.550510257, -8.449489743}
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