d^2+3d-15=0

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Solution for d^2+3d-15=0 equation: 


Simplifying
d2 + 3d + -15 = 0

Reorder the terms:
-15 + 3d + d2 = 0

Solving
-15 + 3d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 3d + 15 + d2 = 0 + 15

Reorder the terms:
-15 + 15 + 3d + d2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 3d + d2 = 0 + 15
3d + d2 = 0 + 15

Combine like terms: 0 + 15 = 15
3d + d2 = 15

The d term is 3d.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3d + 2.25 + d2 = 15 + 2.25

Reorder the terms:
2.25 + 3d + d2 = 15 + 2.25

Combine like terms: 15 + 2.25 = 17.25
2.25 + 3d + d2 = 17.25

Factor a perfect square on the left side:
(d + 1.5)(d + 1.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(d + 1.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
d + 1.5 = 4.153311931

Simplifying
d + 1.5 = 4.153311931

Reorder the terms:
1.5 + d = 4.153311931

Solving
1.5 + d = 4.153311931

Solving for variable 'd'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + d = 4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = 4.153311931 + -1.5
d = 4.153311931 + -1.5

Combine like terms: 4.153311931 + -1.5 = 2.653311931
d = 2.653311931

Simplifying
d = 2.653311931


Subproblem 2
d + 1.5 = -4.153311931

Simplifying
d + 1.5 = -4.153311931

Reorder the terms:
1.5 + d = -4.153311931

Solving
1.5 + d = -4.153311931

Solving for variable 'd'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + d = -4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = -4.153311931 + -1.5
d = -4.153311931 + -1.5

Combine like terms: -4.153311931 + -1.5 = -5.653311931
d = -5.653311931

Simplifying
d = -5.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.653311931, -5.653311931}

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