d^2-20d-15=0

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Solution for d^2-20d-15=0 equation: 


Simplifying
d2 + -20d + -15 = 0

Reorder the terms:
-15 + -20d + d2 = 0

Solving
-15 + -20d + 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 + -20d + 15 + d2 = 0 + 15

Reorder the terms:
-15 + 15 + -20d + d2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -20d + d2 = 0 + 15
-20d + d2 = 0 + 15

Combine like terms: 0 + 15 = 15
-20d + d2 = 15

The d term is -20d.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20d + 100 + d2 = 15 + 100

Reorder the terms:
100 + -20d + d2 = 15 + 100

Combine like terms: 15 + 100 = 115
100 + -20d + d2 = 115

Factor a perfect square on the left side:
(d + -10)(d + -10) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(d + -10) equal to 10.723805295 and -10.723805295.


Subproblem 1
d + -10 = 10.723805295

Simplifying
d + -10 = 10.723805295

Reorder the terms:
-10 + d = 10.723805295

Solving
-10 + d = 10.723805295

Solving for variable 'd'.

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

Add '10' to each side of the equation.
-10 + 10 + d = 10.723805295 + 10

Combine like terms: -10 + 10 = 0
0 + d = 10.723805295 + 10
d = 10.723805295 + 10

Combine like terms: 10.723805295 + 10 = 20.723805295
d = 20.723805295

Simplifying
d = 20.723805295


Subproblem 2
d + -10 = -10.723805295

Simplifying
d + -10 = -10.723805295

Reorder the terms:
-10 + d = -10.723805295

Solving
-10 + d = -10.723805295

Solving for variable 'd'.

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

Add '10' to each side of the equation.
-10 + 10 + d = -10.723805295 + 10

Combine like terms: -10 + 10 = 0
0 + d = -10.723805295 + 10
d = -10.723805295 + 10

Combine like terms: -10.723805295 + 10 = -0.723805295
d = -0.723805295

Simplifying
d = -0.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {20.723805295, -0.723805295}

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