d^2+10d+10=-7

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Solution for d^2+10d+10=-7 equation: 


Simplifying
d2 + 10d + 10 = -7

Reorder the terms:
10 + 10d + d2 = -7

Solving
10 + 10d + d2 = -7

Solving for variable 'd'.

Reorder the terms:
10 + 7 + 10d + d2 = -7 + 7

Combine like terms: 10 + 7 = 17
17 + 10d + d2 = -7 + 7

Combine like terms: -7 + 7 = 0
17 + 10d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 10d + -17 + d2 = 0 + -17

Reorder the terms:
17 + -17 + 10d + d2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 10d + d2 = 0 + -17
10d + d2 = 0 + -17

Combine like terms: 0 + -17 = -17
10d + d2 = -17

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 = -17 + 25

Reorder the terms:
25 + 10d + d2 = -17 + 25

Combine like terms: -17 + 25 = 8
25 + 10d + d2 = 8

Factor a perfect square on the left side:
(d + 5)(d + 5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(d + 5) equal to 2.828427125 and -2.828427125.


Subproblem 1
d + 5 = 2.828427125

Simplifying
d + 5 = 2.828427125

Reorder the terms:
5 + d = 2.828427125

Solving
5 + d = 2.828427125

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 = 2.828427125 + -5

Combine like terms: 5 + -5 = 0
0 + d = 2.828427125 + -5
d = 2.828427125 + -5

Combine like terms: 2.828427125 + -5 = -2.171572875
d = -2.171572875

Simplifying
d = -2.171572875


Subproblem 2
d + 5 = -2.828427125

Simplifying
d + 5 = -2.828427125

Reorder the terms:
5 + d = -2.828427125

Solving
5 + d = -2.828427125

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 = -2.828427125 + -5

Combine like terms: 5 + -5 = 0
0 + d = -2.828427125 + -5
d = -2.828427125 + -5

Combine like terms: -2.828427125 + -5 = -7.828427125
d = -7.828427125

Simplifying
d = -7.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-2.171572875, -7.828427125}

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