(a-10)*(a-10)=200

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Solution for (a-10)*(a-10)=200 equation: 


Simplifying
(a + -10)(a + -10) = 200

Reorder the terms:
(-10 + a)(a + -10) = 200

Reorder the terms:
(-10 + a)(-10 + a) = 200

Multiply (-10 + a) * (-10 + a)
(-10(-10 + a) + a(-10 + a)) = 200
((-10 * -10 + a * -10) + a(-10 + a)) = 200
((100 + -10a) + a(-10 + a)) = 200
(100 + -10a + (-10 * a + a * a)) = 200
(100 + -10a + (-10a + a2)) = 200

Combine like terms: -10a + -10a = -20a
(100 + -20a + a2) = 200

Solving
100 + -20a + a2 = 200

Solving for variable 'a'.

Reorder the terms:
100 + -200 + -20a + a2 = 200 + -200

Combine like terms: 100 + -200 = -100
-100 + -20a + a2 = 200 + -200

Combine like terms: 200 + -200 = 0
-100 + -20a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -20a + 100 + a2 = 0 + 100

Reorder the terms:
-100 + 100 + -20a + a2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -20a + a2 = 0 + 100
-20a + a2 = 0 + 100

Combine like terms: 0 + 100 = 100
-20a + a2 = 100

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

Add '100' to each side of the equation.
-20a + 100 + a2 = 100 + 100

Reorder the terms:
100 + -20a + a2 = 100 + 100

Combine like terms: 100 + 100 = 200
100 + -20a + a2 = 200

Factor a perfect square on the left side:
(a + -10)(a + -10) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(a + -10) equal to 14.142135624 and -14.142135624.


Subproblem 1
a + -10 = 14.142135624

Simplifying
a + -10 = 14.142135624

Reorder the terms:
-10 + a = 14.142135624

Solving
-10 + a = 14.142135624

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = 14.142135624 + 10

Combine like terms: -10 + 10 = 0
0 + a = 14.142135624 + 10
a = 14.142135624 + 10

Combine like terms: 14.142135624 + 10 = 24.142135624
a = 24.142135624

Simplifying
a = 24.142135624


Subproblem 2
a + -10 = -14.142135624

Simplifying
a + -10 = -14.142135624

Reorder the terms:
-10 + a = -14.142135624

Solving
-10 + a = -14.142135624

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = -14.142135624 + 10

Combine like terms: -10 + 10 = 0
0 + a = -14.142135624 + 10
a = -14.142135624 + 10

Combine like terms: -14.142135624 + 10 = -4.142135624
a = -4.142135624

Simplifying
a = -4.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {24.142135624, -4.142135624}

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