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Simplifying b2 + 16b + 26 = -3 Reorder the terms: 26 + 16b + b2 = -3 Solving 26 + 16b + b2 = -3 Solving for variable 'b'. Reorder the terms: 26 + 3 + 16b + b2 = -3 + 3 Combine like terms: 26 + 3 = 29 29 + 16b + b2 = -3 + 3 Combine like terms: -3 + 3 = 0 29 + 16b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 16b + -29 + b2 = 0 + -29 Reorder the terms: 29 + -29 + 16b + b2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 16b + b2 = 0 + -29 16b + b2 = 0 + -29 Combine like terms: 0 + -29 = -29 16b + b2 = -29 The b term is 16b. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16b + 64 + b2 = -29 + 64 Reorder the terms: 64 + 16b + b2 = -29 + 64 Combine like terms: -29 + 64 = 35 64 + 16b + b2 = 35 Factor a perfect square on the left side: (b + 8)(b + 8) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (b + 8) equal to 5.916079783 and -5.916079783.Subproblem 1
b + 8 = 5.916079783 Simplifying b + 8 = 5.916079783 Reorder the terms: 8 + b = 5.916079783 Solving 8 + b = 5.916079783 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + b = 5.916079783 + -8 Combine like terms: 8 + -8 = 0 0 + b = 5.916079783 + -8 b = 5.916079783 + -8 Combine like terms: 5.916079783 + -8 = -2.083920217 b = -2.083920217 Simplifying b = -2.083920217Subproblem 2
b + 8 = -5.916079783 Simplifying b + 8 = -5.916079783 Reorder the terms: 8 + b = -5.916079783 Solving 8 + b = -5.916079783 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + b = -5.916079783 + -8 Combine like terms: 8 + -8 = 0 0 + b = -5.916079783 + -8 b = -5.916079783 + -8 Combine like terms: -5.916079783 + -8 = -13.916079783 b = -13.916079783 Simplifying b = -13.916079783Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.083920217, -13.916079783}
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