d^2+5d-6=9

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Solution for d^2+5d-6=9 equation: 


Simplifying
d2 + 5d + -6 = 9

Reorder the terms:
-6 + 5d + d2 = 9

Solving
-6 + 5d + d2 = 9

Solving for variable 'd'.

Reorder the terms:
-6 + -9 + 5d + d2 = 9 + -9

Combine like terms: -6 + -9 = -15
-15 + 5d + d2 = 9 + -9

Combine like terms: 9 + -9 = 0
-15 + 5d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 5d + 15 + d2 = 0 + 15

Reorder the terms:
-15 + 15 + 5d + d2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 5d + d2 = 0 + 15
5d + d2 = 0 + 15

Combine like terms: 0 + 15 = 15
5d + d2 = 15

The d term is 5d.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5d + 6.25 + d2 = 15 + 6.25

Reorder the terms:
6.25 + 5d + d2 = 15 + 6.25

Combine like terms: 15 + 6.25 = 21.25
6.25 + 5d + d2 = 21.25

Factor a perfect square on the left side:
(d + 2.5)(d + 2.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(d + 2.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
d + 2.5 = 4.609772229

Simplifying
d + 2.5 = 4.609772229

Reorder the terms:
2.5 + d = 4.609772229

Solving
2.5 + d = 4.609772229

Solving for variable 'd'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + d = 4.609772229 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + d = 4.609772229 + -2.5
d = 4.609772229 + -2.5

Combine like terms: 4.609772229 + -2.5 = 2.109772229
d = 2.109772229

Simplifying
d = 2.109772229


Subproblem 2
d + 2.5 = -4.609772229

Simplifying
d + 2.5 = -4.609772229

Reorder the terms:
2.5 + d = -4.609772229

Solving
2.5 + d = -4.609772229

Solving for variable 'd'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + d = -4.609772229 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + d = -4.609772229 + -2.5
d = -4.609772229 + -2.5

Combine like terms: -4.609772229 + -2.5 = -7.109772229
d = -7.109772229

Simplifying
d = -7.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.109772229, -7.109772229}

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