2d^2+72d-1440=0

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Solution for 2d^2+72d-1440=0 equation: 


Simplifying
2d2 + 72d + -1440 = 0

Reorder the terms:
-1440 + 72d + 2d2 = 0

Solving
-1440 + 72d + 2d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-720 + 36d + d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-720 + 36d + d2)' equal to zero and attempt to solve:

Simplifying
-720 + 36d + d2 = 0

Solving
-720 + 36d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '720' to each side of the equation.
-720 + 36d + 720 + d2 = 0 + 720

Reorder the terms:
-720 + 720 + 36d + d2 = 0 + 720

Combine like terms: -720 + 720 = 0
0 + 36d + d2 = 0 + 720
36d + d2 = 0 + 720

Combine like terms: 0 + 720 = 720
36d + d2 = 720

The d term is 36d.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36d + 324 + d2 = 720 + 324

Reorder the terms:
324 + 36d + d2 = 720 + 324

Combine like terms: 720 + 324 = 1044
324 + 36d + d2 = 1044

Factor a perfect square on the left side:
(d + 18)(d + 18) = 1044

Calculate the square root of the right side: 32.310988843

Break this problem into two subproblems by setting 
(d + 18) equal to 32.310988843 and -32.310988843.


Subproblem 1
d + 18 = 32.310988843

Simplifying
d + 18 = 32.310988843

Reorder the terms:
18 + d = 32.310988843

Solving
18 + d = 32.310988843

Solving for variable 'd'.

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

Add '-18' to each side of the equation.
18 + -18 + d = 32.310988843 + -18

Combine like terms: 18 + -18 = 0
0 + d = 32.310988843 + -18
d = 32.310988843 + -18

Combine like terms: 32.310988843 + -18 = 14.310988843
d = 14.310988843

Simplifying
d = 14.310988843


Subproblem 2
d + 18 = -32.310988843

Simplifying
d + 18 = -32.310988843

Reorder the terms:
18 + d = -32.310988843

Solving
18 + d = -32.310988843

Solving for variable 'd'.

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

Add '-18' to each side of the equation.
18 + -18 + d = -32.310988843 + -18

Combine like terms: 18 + -18 = 0
0 + d = -32.310988843 + -18
d = -32.310988843 + -18

Combine like terms: -32.310988843 + -18 = -50.310988843
d = -50.310988843

Simplifying
d = -50.310988843


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {14.310988843, -50.310988843}
Solution
d = {14.310988843, -50.310988843}

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