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Simplifying b2 + 3b + -96.89 = 0 Reorder the terms: -96.89 + 3b + b2 = 0 Solving -96.89 + 3b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '96.89' to each side of the equation. -96.89 + 3b + 96.89 + b2 = 0 + 96.89 Reorder the terms: -96.89 + 96.89 + 3b + b2 = 0 + 96.89 Combine like terms: -96.89 + 96.89 = 0.00 0.00 + 3b + b2 = 0 + 96.89 3b + b2 = 0 + 96.89 Combine like terms: 0 + 96.89 = 96.89 3b + b2 = 96.89 The b term is 3b. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3b + 2.25 + b2 = 96.89 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 96.89 + 2.25 Combine like terms: 96.89 + 2.25 = 99.14 2.25 + 3b + b2 = 99.14 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 99.14 Calculate the square root of the right side: 9.95690715 Break this problem into two subproblems by setting (b + 1.5) equal to 9.95690715 and -9.95690715.Subproblem 1
b + 1.5 = 9.95690715 Simplifying b + 1.5 = 9.95690715 Reorder the terms: 1.5 + b = 9.95690715 Solving 1.5 + b = 9.95690715 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = 9.95690715 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 9.95690715 + -1.5 b = 9.95690715 + -1.5 Combine like terms: 9.95690715 + -1.5 = 8.45690715 b = 8.45690715 Simplifying b = 8.45690715Subproblem 2
b + 1.5 = -9.95690715 Simplifying b + 1.5 = -9.95690715 Reorder the terms: 1.5 + b = -9.95690715 Solving 1.5 + b = -9.95690715 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = -9.95690715 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -9.95690715 + -1.5 b = -9.95690715 + -1.5 Combine like terms: -9.95690715 + -1.5 = -11.45690715 b = -11.45690715 Simplifying b = -11.45690715Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.45690715, -11.45690715}
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