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Simplifying b2 + 12b + -378 = 0 Reorder the terms: -378 + 12b + b2 = 0 Solving -378 + 12b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '378' to each side of the equation. -378 + 12b + 378 + b2 = 0 + 378 Reorder the terms: -378 + 378 + 12b + b2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + 12b + b2 = 0 + 378 12b + b2 = 0 + 378 Combine like terms: 0 + 378 = 378 12b + b2 = 378 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 = 378 + 36 Reorder the terms: 36 + 12b + b2 = 378 + 36 Combine like terms: 378 + 36 = 414 36 + 12b + b2 = 414 Factor a perfect square on the left side: (b + 6)(b + 6) = 414 Calculate the square root of the right side: 20.346989949 Break this problem into two subproblems by setting (b + 6) equal to 20.346989949 and -20.346989949.Subproblem 1
b + 6 = 20.346989949 Simplifying b + 6 = 20.346989949 Reorder the terms: 6 + b = 20.346989949 Solving 6 + b = 20.346989949 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 = 20.346989949 + -6 Combine like terms: 6 + -6 = 0 0 + b = 20.346989949 + -6 b = 20.346989949 + -6 Combine like terms: 20.346989949 + -6 = 14.346989949 b = 14.346989949 Simplifying b = 14.346989949Subproblem 2
b + 6 = -20.346989949 Simplifying b + 6 = -20.346989949 Reorder the terms: 6 + b = -20.346989949 Solving 6 + b = -20.346989949 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 = -20.346989949 + -6 Combine like terms: 6 + -6 = 0 0 + b = -20.346989949 + -6 b = -20.346989949 + -6 Combine like terms: -20.346989949 + -6 = -26.346989949 b = -26.346989949 Simplifying b = -26.346989949Solution
The solution to the problem is based on the solutions from the subproblems. b = {14.346989949, -26.346989949}
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