2(d^2-10d+25)=30

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Solution for 2(d^2-10d+25)=30 equation: 


Simplifying
2(d2 + -10d + 25) = 30

Reorder the terms:
2(25 + -10d + d2) = 30
(25 * 2 + -10d * 2 + d2 * 2) = 30
(50 + -20d + 2d2) = 30

Solving
50 + -20d + 2d2 = 30

Solving for variable 'd'.

Reorder the terms:
50 + -30 + -20d + 2d2 = 30 + -30

Combine like terms: 50 + -30 = 20
20 + -20d + 2d2 = 30 + -30

Combine like terms: 30 + -30 = 0
20 + -20d + 2d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -10d + d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -10d + d2)' equal to zero and attempt to solve:

Simplifying
10 + -10d + d2 = 0

Solving
10 + -10d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -10d + -10 + d2 = 0 + -10

Reorder the terms:
10 + -10 + -10d + d2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -10d + d2 = 0 + -10
-10d + d2 = 0 + -10

Combine like terms: 0 + -10 = -10
-10d + d2 = -10

The d term is -10d.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10d + 25 + d2 = -10 + 25

Reorder the terms:
25 + -10d + d2 = -10 + 25

Combine like terms: -10 + 25 = 15
25 + -10d + d2 = 15

Factor a perfect square on the left side:
(d + -5)(d + -5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(d + -5) equal to 3.872983346 and -3.872983346.


Subproblem 1
d + -5 = 3.872983346

Simplifying
d + -5 = 3.872983346

Reorder the terms:
-5 + d = 3.872983346

Solving
-5 + d = 3.872983346

Solving for variable 'd'.

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

Add '5' to each side of the equation.
-5 + 5 + d = 3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + d = 3.872983346 + 5
d = 3.872983346 + 5

Combine like terms: 3.872983346 + 5 = 8.872983346
d = 8.872983346

Simplifying
d = 8.872983346


Subproblem 2
d + -5 = -3.872983346

Simplifying
d + -5 = -3.872983346

Reorder the terms:
-5 + d = -3.872983346

Solving
-5 + d = -3.872983346

Solving for variable 'd'.

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

Add '5' to each side of the equation.
-5 + 5 + d = -3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + d = -3.872983346 + 5
d = -3.872983346 + 5

Combine like terms: -3.872983346 + 5 = 1.127016654
d = 1.127016654

Simplifying
d = 1.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {8.872983346, 1.127016654}
Solution
d = {8.872983346, 1.127016654}

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