3d^2-48d-69=0

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Solution for 3d^2-48d-69=0 equation: 


Simplifying
3d2 + -48d + -69 = 0

Reorder the terms:
-69 + -48d + 3d2 = 0

Solving
-69 + -48d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-23 + -16d + d2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-23 + -16d + d2)' equal to zero and attempt to solve:

Simplifying
-23 + -16d + d2 = 0

Solving
-23 + -16d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -16d + 23 + d2 = 0 + 23

Reorder the terms:
-23 + 23 + -16d + d2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -16d + d2 = 0 + 23
-16d + d2 = 0 + 23

Combine like terms: 0 + 23 = 23
-16d + d2 = 23

The d term is -16d.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16d + 64 + d2 = 23 + 64

Reorder the terms:
64 + -16d + d2 = 23 + 64

Combine like terms: 23 + 64 = 87
64 + -16d + d2 = 87

Factor a perfect square on the left side:
(d + -8)(d + -8) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(d + -8) equal to 9.327379053 and -9.327379053.


Subproblem 1
d + -8 = 9.327379053

Simplifying
d + -8 = 9.327379053

Reorder the terms:
-8 + d = 9.327379053

Solving
-8 + d = 9.327379053

Solving for variable 'd'.

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

Add '8' to each side of the equation.
-8 + 8 + d = 9.327379053 + 8

Combine like terms: -8 + 8 = 0
0 + d = 9.327379053 + 8
d = 9.327379053 + 8

Combine like terms: 9.327379053 + 8 = 17.327379053
d = 17.327379053

Simplifying
d = 17.327379053


Subproblem 2
d + -8 = -9.327379053

Simplifying
d + -8 = -9.327379053

Reorder the terms:
-8 + d = -9.327379053

Solving
-8 + d = -9.327379053

Solving for variable 'd'.

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

Add '8' to each side of the equation.
-8 + 8 + d = -9.327379053 + 8

Combine like terms: -8 + 8 = 0
0 + d = -9.327379053 + 8
d = -9.327379053 + 8

Combine like terms: -9.327379053 + 8 = -1.327379053
d = -1.327379053

Simplifying
d = -1.327379053


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {17.327379053, -1.327379053}
Solution
d = {17.327379053, -1.327379053}

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