a^2-20a+52=8

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Solution for a^2-20a+52=8 equation:


Simplifying
a2 + -20a + 52 = 8

Reorder the terms:
52 + -20a + a2 = 8

Solving
52 + -20a + a2 = 8

Solving for variable 'a'.

Reorder the terms:
52 + -8 + -20a + a2 = 8 + -8

Combine like terms: 52 + -8 = 44
44 + -20a + a2 = 8 + -8

Combine like terms: 8 + -8 = 0
44 + -20a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -20a + -44 + a2 = 0 + -44

Reorder the terms:
44 + -44 + -20a + a2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -20a + a2 = 0 + -44
-20a + a2 = 0 + -44

Combine like terms: 0 + -44 = -44
-20a + a2 = -44

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 = -44 + 100

Reorder the terms:
100 + -20a + a2 = -44 + 100

Combine like terms: -44 + 100 = 56
100 + -20a + a2 = 56

Factor a perfect square on the left side:
(a + -10)(a + -10) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(a + -10) equal to 7.483314774 and -7.483314774.

Subproblem 1

a + -10 = 7.483314774 Simplifying a + -10 = 7.483314774 Reorder the terms: -10 + a = 7.483314774 Solving -10 + a = 7.483314774 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 = 7.483314774 + 10 Combine like terms: -10 + 10 = 0 0 + a = 7.483314774 + 10 a = 7.483314774 + 10 Combine like terms: 7.483314774 + 10 = 17.483314774 a = 17.483314774 Simplifying a = 17.483314774

Subproblem 2

a + -10 = -7.483314774 Simplifying a + -10 = -7.483314774 Reorder the terms: -10 + a = -7.483314774 Solving -10 + a = -7.483314774 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 = -7.483314774 + 10 Combine like terms: -10 + 10 = 0 0 + a = -7.483314774 + 10 a = -7.483314774 + 10 Combine like terms: -7.483314774 + 10 = 2.516685226 a = 2.516685226 Simplifying a = 2.516685226

Solution

The solution to the problem is based on the solutions from the subproblems. a = {17.483314774, 2.516685226}

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