d^2-10d+26=8

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Solution for d^2-10d+26=8 equation: 


Simplifying
d2 + -10d + 26 = 8

Reorder the terms:
26 + -10d + d2 = 8

Solving
26 + -10d + d2 = 8

Solving for variable 'd'.

Reorder the terms:
26 + -8 + -10d + d2 = 8 + -8

Combine like terms: 26 + -8 = 18
18 + -10d + d2 = 8 + -8

Combine like terms: 8 + -8 = 0
18 + -10d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10d + -18 + d2 = 0 + -18

Reorder the terms:
18 + -18 + -10d + d2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10d + d2 = 0 + -18
-10d + d2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10d + d2 = -18

The d term is -10d.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10d + 25 + d2 = -18 + 25

Reorder the terms:
25 + -10d + d2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10d + d2 = 7

Factor a perfect square on the left side:
(d + -5)(d + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(d + -5) equal to 2.645751311 and -2.645751311.


Subproblem 1
d + -5 = 2.645751311

Simplifying
d + -5 = 2.645751311

Reorder the terms:
-5 + d = 2.645751311

Solving
-5 + d = 2.645751311

Solving for variable 'd'.

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

Add '5' to each side of the equation.
-5 + 5 + d = 2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + d = 2.645751311 + 5
d = 2.645751311 + 5

Combine like terms: 2.645751311 + 5 = 7.645751311
d = 7.645751311

Simplifying
d = 7.645751311


Subproblem 2
d + -5 = -2.645751311

Simplifying
d + -5 = -2.645751311

Reorder the terms:
-5 + d = -2.645751311

Solving
-5 + d = -2.645751311

Solving for variable 'd'.

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

Add '5' to each side of the equation.
-5 + 5 + d = -2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + d = -2.645751311 + 5
d = -2.645751311 + 5

Combine like terms: -2.645751311 + 5 = 2.354248689
d = 2.354248689

Simplifying
d = 2.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {7.645751311, 2.354248689}

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