a^2-20a-52=0

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Solution for a^2-20a-52=0 equation:


Simplifying
a2 + -20a + -52 = 0

Reorder the terms:
-52 + -20a + a2 = 0

Solving
-52 + -20a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -20a + 52 + a2 = 0 + 52

Reorder the terms:
-52 + 52 + -20a + a2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -20a + a2 = 0 + 52
-20a + a2 = 0 + 52

Combine like terms: 0 + 52 = 52
-20a + a2 = 52

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 = 52 + 100

Reorder the terms:
100 + -20a + a2 = 52 + 100

Combine like terms: 52 + 100 = 152
100 + -20a + a2 = 152

Factor a perfect square on the left side:
(a + -10)(a + -10) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(a + -10) equal to 12.328828006 and -12.328828006.

Subproblem 1

a + -10 = 12.328828006 Simplifying a + -10 = 12.328828006 Reorder the terms: -10 + a = 12.328828006 Solving -10 + a = 12.328828006 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 = 12.328828006 + 10 Combine like terms: -10 + 10 = 0 0 + a = 12.328828006 + 10 a = 12.328828006 + 10 Combine like terms: 12.328828006 + 10 = 22.328828006 a = 22.328828006 Simplifying a = 22.328828006

Subproblem 2

a + -10 = -12.328828006 Simplifying a + -10 = -12.328828006 Reorder the terms: -10 + a = -12.328828006 Solving -10 + a = -12.328828006 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 = -12.328828006 + 10 Combine like terms: -10 + 10 = 0 0 + a = -12.328828006 + 10 a = -12.328828006 + 10 Combine like terms: -12.328828006 + 10 = -2.328828006 a = -2.328828006 Simplifying a = -2.328828006

Solution

The solution to the problem is based on the solutions from the subproblems. a = {22.328828006, -2.328828006}

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