b^2-14b-78=0

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Solution for b^2-14b-78=0 equation:


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 = 18.26942767

Subproblem 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 = -4.26942767

Solution

The solution to the problem is based on the solutions from the subproblems. b = {18.26942767, -4.26942767}

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