d^2-3d-46=0

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Solution for d^2-3d-46=0 equation: 


Simplifying
d2 + -3d + -46 = 0

Reorder the terms:
-46 + -3d + d2 = 0

Solving
-46 + -3d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + -3d + 46 + d2 = 0 + 46

Reorder the terms:
-46 + 46 + -3d + d2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -3d + d2 = 0 + 46
-3d + d2 = 0 + 46

Combine like terms: 0 + 46 = 46
-3d + d2 = 46

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 = 46 + 2.25

Reorder the terms:
2.25 + -3d + d2 = 46 + 2.25

Combine like terms: 46 + 2.25 = 48.25
2.25 + -3d + d2 = 48.25

Factor a perfect square on the left side:
(d + -1.5)(d + -1.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(d + -1.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
d + -1.5 = 6.946221995

Simplifying
d + -1.5 = 6.946221995

Reorder the terms:
-1.5 + d = 6.946221995

Solving
-1.5 + d = 6.946221995

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 = 6.946221995 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + d = 6.946221995 + 1.5
d = 6.946221995 + 1.5

Combine like terms: 6.946221995 + 1.5 = 8.446221995
d = 8.446221995

Simplifying
d = 8.446221995


Subproblem 2
d + -1.5 = -6.946221995

Simplifying
d + -1.5 = -6.946221995

Reorder the terms:
-1.5 + d = -6.946221995

Solving
-1.5 + d = -6.946221995

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 = -6.946221995 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + d = -6.946221995 + 1.5
d = -6.946221995 + 1.5

Combine like terms: -6.946221995 + 1.5 = -5.446221995
d = -5.446221995

Simplifying
d = -5.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {8.446221995, -5.446221995}

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