d^2+18d+13=0

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Solution for d^2+18d+13=0 equation: 


Simplifying
d2 + 18d + 13 = 0

Reorder the terms:
13 + 18d + d2 = 0

Solving
13 + 18d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 18d + -13 + d2 = 0 + -13

Reorder the terms:
13 + -13 + 18d + d2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 18d + d2 = 0 + -13
18d + d2 = 0 + -13

Combine like terms: 0 + -13 = -13
18d + d2 = -13

The d term is 18d.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18d + 81 + d2 = -13 + 81

Reorder the terms:
81 + 18d + d2 = -13 + 81

Combine like terms: -13 + 81 = 68
81 + 18d + d2 = 68

Factor a perfect square on the left side:
(d + 9)(d + 9) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(d + 9) equal to 8.246211251 and -8.246211251.


Subproblem 1
d + 9 = 8.246211251

Simplifying
d + 9 = 8.246211251

Reorder the terms:
9 + d = 8.246211251

Solving
9 + d = 8.246211251

Solving for variable 'd'.

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

Add '-9' to each side of the equation.
9 + -9 + d = 8.246211251 + -9

Combine like terms: 9 + -9 = 0
0 + d = 8.246211251 + -9
d = 8.246211251 + -9

Combine like terms: 8.246211251 + -9 = -0.753788749
d = -0.753788749

Simplifying
d = -0.753788749


Subproblem 2
d + 9 = -8.246211251

Simplifying
d + 9 = -8.246211251

Reorder the terms:
9 + d = -8.246211251

Solving
9 + d = -8.246211251

Solving for variable 'd'.

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

Add '-9' to each side of the equation.
9 + -9 + d = -8.246211251 + -9

Combine like terms: 9 + -9 = 0
0 + d = -8.246211251 + -9
d = -8.246211251 + -9

Combine like terms: -8.246211251 + -9 = -17.246211251
d = -17.246211251

Simplifying
d = -17.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.753788749, -17.246211251}

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