a^2-22a+121=3

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Solution for a^2-22a+121=3 equation:


Simplifying
a2 + -22a + 121 = 3

Reorder the terms:
121 + -22a + a2 = 3

Solving
121 + -22a + a2 = 3

Solving for variable 'a'.

Reorder the terms:
121 + -3 + -22a + a2 = 3 + -3

Combine like terms: 121 + -3 = 118
118 + -22a + a2 = 3 + -3

Combine like terms: 3 + -3 = 0
118 + -22a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-118' to each side of the equation.
118 + -22a + -118 + a2 = 0 + -118

Reorder the terms:
118 + -118 + -22a + a2 = 0 + -118

Combine like terms: 118 + -118 = 0
0 + -22a + a2 = 0 + -118
-22a + a2 = 0 + -118

Combine like terms: 0 + -118 = -118
-22a + a2 = -118

The a term is -22a.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22a + 121 + a2 = -118 + 121

Reorder the terms:
121 + -22a + a2 = -118 + 121

Combine like terms: -118 + 121 = 3
121 + -22a + a2 = 3

Factor a perfect square on the left side:
(a + -11)(a + -11) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + -11) equal to 1.732050808 and -1.732050808.

Subproblem 1

a + -11 = 1.732050808 Simplifying a + -11 = 1.732050808 Reorder the terms: -11 + a = 1.732050808 Solving -11 + a = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + a = 1.732050808 + 11 Combine like terms: -11 + 11 = 0 0 + a = 1.732050808 + 11 a = 1.732050808 + 11 Combine like terms: 1.732050808 + 11 = 12.732050808 a = 12.732050808 Simplifying a = 12.732050808

Subproblem 2

a + -11 = -1.732050808 Simplifying a + -11 = -1.732050808 Reorder the terms: -11 + a = -1.732050808 Solving -11 + a = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + a = -1.732050808 + 11 Combine like terms: -11 + 11 = 0 0 + a = -1.732050808 + 11 a = -1.732050808 + 11 Combine like terms: -1.732050808 + 11 = 9.267949192 a = 9.267949192 Simplifying a = 9.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.732050808, 9.267949192}

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