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Simplifying b2 + 10b + -79 = 0 Reorder the terms: -79 + 10b + b2 = 0 Solving -79 + 10b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + 10b + 79 + b2 = 0 + 79 Reorder the terms: -79 + 79 + 10b + b2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + 10b + b2 = 0 + 79 10b + b2 = 0 + 79 Combine like terms: 0 + 79 = 79 10b + b2 = 79 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = 79 + 25 Reorder the terms: 25 + 10b + b2 = 79 + 25 Combine like terms: 79 + 25 = 104 25 + 10b + b2 = 104 Factor a perfect square on the left side: (b + 5)(b + 5) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (b + 5) equal to 10.198039027 and -10.198039027.Subproblem 1
b + 5 = 10.198039027 Simplifying b + 5 = 10.198039027 Reorder the terms: 5 + b = 10.198039027 Solving 5 + b = 10.198039027 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 10.198039027 + -5 Combine like terms: 5 + -5 = 0 0 + b = 10.198039027 + -5 b = 10.198039027 + -5 Combine like terms: 10.198039027 + -5 = 5.198039027 b = 5.198039027 Simplifying b = 5.198039027Subproblem 2
b + 5 = -10.198039027 Simplifying b + 5 = -10.198039027 Reorder the terms: 5 + b = -10.198039027 Solving 5 + b = -10.198039027 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -10.198039027 + -5 Combine like terms: 5 + -5 = 0 0 + b = -10.198039027 + -5 b = -10.198039027 + -5 Combine like terms: -10.198039027 + -5 = -15.198039027 b = -15.198039027 Simplifying b = -15.198039027Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.198039027, -15.198039027}
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