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Simplifying b2 + -14b + -78 = 0 Reorder the terms: -78 + -14b + b2 = 0 Solving -78 + -14b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -14b + 78 + b2 = 0 + 78 Reorder the terms: -78 + 78 + -14b + b2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -14b + b2 = 0 + 78 -14b + b2 = 0 + 78 Combine like terms: 0 + 78 = 78 -14b + b2 = 78 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 = 78 + 49 Reorder the terms: 49 + -14b + b2 = 78 + 49 Combine like terms: 78 + 49 = 127 49 + -14b + b2 = 127 Factor a perfect square on the left side: (b + -7)(b + -7) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (b + -7) equal to 11.26942767 and -11.26942767.Subproblem 1
b + -7 = 11.26942767 Simplifying b + -7 = 11.26942767 Reorder the terms: -7 + b = 11.26942767 Solving -7 + b = 11.26942767 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 = 11.26942767 + 7 Combine like terms: -7 + 7 = 0 0 + b = 11.26942767 + 7 b = 11.26942767 + 7 Combine like terms: 11.26942767 + 7 = 18.26942767 b = 18.26942767 Simplifying b = 18.26942767Subproblem 2
b + -7 = -11.26942767 Simplifying b + -7 = -11.26942767 Reorder the terms: -7 + b = -11.26942767 Solving -7 + b = -11.26942767 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 = -11.26942767 + 7 Combine like terms: -7 + 7 = 0 0 + b = -11.26942767 + 7 b = -11.26942767 + 7 Combine like terms: -11.26942767 + 7 = -4.26942767 b = -4.26942767 Simplifying b = -4.26942767Solution
The solution to the problem is based on the solutions from the subproblems. b = {18.26942767, -4.26942767}
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