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Simplifying b2 + 14b + -61 = 0 Reorder the terms: -61 + 14b + b2 = 0 Solving -61 + 14b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 14b + 61 + b2 = 0 + 61 Reorder the terms: -61 + 61 + 14b + b2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 14b + b2 = 0 + 61 14b + b2 = 0 + 61 Combine like terms: 0 + 61 = 61 14b + b2 = 61 The b term is 14b. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14b + 49 + b2 = 61 + 49 Reorder the terms: 49 + 14b + b2 = 61 + 49 Combine like terms: 61 + 49 = 110 49 + 14b + b2 = 110 Factor a perfect square on the left side: (b + 7)(b + 7) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (b + 7) equal to 10.488088482 and -10.488088482.Subproblem 1
b + 7 = 10.488088482 Simplifying b + 7 = 10.488088482 Reorder the terms: 7 + b = 10.488088482 Solving 7 + b = 10.488088482 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = 10.488088482 + -7 Combine like terms: 7 + -7 = 0 0 + b = 10.488088482 + -7 b = 10.488088482 + -7 Combine like terms: 10.488088482 + -7 = 3.488088482 b = 3.488088482 Simplifying b = 3.488088482Subproblem 2
b + 7 = -10.488088482 Simplifying b + 7 = -10.488088482 Reorder the terms: 7 + b = -10.488088482 Solving 7 + b = -10.488088482 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = -10.488088482 + -7 Combine like terms: 7 + -7 = 0 0 + b = -10.488088482 + -7 b = -10.488088482 + -7 Combine like terms: -10.488088482 + -7 = -17.488088482 b = -17.488088482 Simplifying b = -17.488088482Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.488088482, -17.488088482}
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