a^2-20a-53=9

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Solution for a^2-20a-53=9 equation:


Simplifying
a2 + -20a + -53 = 9

Reorder the terms:
-53 + -20a + a2 = 9

Solving
-53 + -20a + a2 = 9

Solving for variable 'a'.

Reorder the terms:
-53 + -9 + -20a + a2 = 9 + -9

Combine like terms: -53 + -9 = -62
-62 + -20a + a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-62 + -20a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -20a + 62 + a2 = 0 + 62

Reorder the terms:
-62 + 62 + -20a + a2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -20a + a2 = 0 + 62
-20a + a2 = 0 + 62

Combine like terms: 0 + 62 = 62
-20a + a2 = 62

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 = 62 + 100

Reorder the terms:
100 + -20a + a2 = 62 + 100

Combine like terms: 62 + 100 = 162
100 + -20a + a2 = 162

Factor a perfect square on the left side:
(a + -10)(a + -10) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(a + -10) equal to 12.727922061 and -12.727922061.

Subproblem 1

a + -10 = 12.727922061 Simplifying a + -10 = 12.727922061 Reorder the terms: -10 + a = 12.727922061 Solving -10 + a = 12.727922061 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 = 12.727922061 + 10 Combine like terms: -10 + 10 = 0 0 + a = 12.727922061 + 10 a = 12.727922061 + 10 Combine like terms: 12.727922061 + 10 = 22.727922061 a = 22.727922061 Simplifying a = 22.727922061

Subproblem 2

a + -10 = -12.727922061 Simplifying a + -10 = -12.727922061 Reorder the terms: -10 + a = -12.727922061 Solving -10 + a = -12.727922061 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 = -12.727922061 + 10 Combine like terms: -10 + 10 = 0 0 + a = -12.727922061 + 10 a = -12.727922061 + 10 Combine like terms: -12.727922061 + 10 = -2.727922061 a = -2.727922061 Simplifying a = -2.727922061

Solution

The solution to the problem is based on the solutions from the subproblems. a = {22.727922061, -2.727922061}

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