d^2-14d-22=0

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Solution for d^2-14d-22=0 equation: 


Simplifying
d2 + -14d + -22 = 0

Reorder the terms:
-22 + -14d + d2 = 0

Solving
-22 + -14d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -14d + 22 + d2 = 0 + 22

Reorder the terms:
-22 + 22 + -14d + d2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -14d + d2 = 0 + 22
-14d + d2 = 0 + 22

Combine like terms: 0 + 22 = 22
-14d + d2 = 22

The d term is -14d.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14d + 49 + d2 = 22 + 49

Reorder the terms:
49 + -14d + d2 = 22 + 49

Combine like terms: 22 + 49 = 71
49 + -14d + d2 = 71

Factor a perfect square on the left side:
(d + -7)(d + -7) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(d + -7) equal to 8.426149773 and -8.426149773.


Subproblem 1
d + -7 = 8.426149773

Simplifying
d + -7 = 8.426149773

Reorder the terms:
-7 + d = 8.426149773

Solving
-7 + d = 8.426149773

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + d = 8.426149773 + 7

Combine like terms: -7 + 7 = 0
0 + d = 8.426149773 + 7
d = 8.426149773 + 7

Combine like terms: 8.426149773 + 7 = 15.426149773
d = 15.426149773

Simplifying
d = 15.426149773


Subproblem 2
d + -7 = -8.426149773

Simplifying
d + -7 = -8.426149773

Reorder the terms:
-7 + d = -8.426149773

Solving
-7 + d = -8.426149773

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + d = -8.426149773 + 7

Combine like terms: -7 + 7 = 0
0 + d = -8.426149773 + 7
d = -8.426149773 + 7

Combine like terms: -8.426149773 + 7 = -1.426149773
d = -1.426149773

Simplifying
d = -1.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {15.426149773, -1.426149773}

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