c^2-22c+9=0

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Solution for c^2-22c+9=0 equation:


Simplifying
c2 + -22c + 9 = 0

Reorder the terms:
9 + -22c + c2 = 0

Solving
9 + -22c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -22c + -9 + c2 = 0 + -9

Reorder the terms:
9 + -9 + -22c + c2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -22c + c2 = 0 + -9
-22c + c2 = 0 + -9

Combine like terms: 0 + -9 = -9
-22c + c2 = -9

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

Add '121' to each side of the equation.
-22c + 121 + c2 = -9 + 121

Reorder the terms:
121 + -22c + c2 = -9 + 121

Combine like terms: -9 + 121 = 112
121 + -22c + c2 = 112

Factor a perfect square on the left side:
(c + -11)(c + -11) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(c + -11) equal to 10.583005244 and -10.583005244.

Subproblem 1

c + -11 = 10.583005244 Simplifying c + -11 = 10.583005244 Reorder the terms: -11 + c = 10.583005244 Solving -11 + c = 10.583005244 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + c = 10.583005244 + 11 Combine like terms: -11 + 11 = 0 0 + c = 10.583005244 + 11 c = 10.583005244 + 11 Combine like terms: 10.583005244 + 11 = 21.583005244 c = 21.583005244 Simplifying c = 21.583005244

Subproblem 2

c + -11 = -10.583005244 Simplifying c + -11 = -10.583005244 Reorder the terms: -11 + c = -10.583005244 Solving -11 + c = -10.583005244 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + c = -10.583005244 + 11 Combine like terms: -11 + 11 = 0 0 + c = -10.583005244 + 11 c = -10.583005244 + 11 Combine like terms: -10.583005244 + 11 = 0.416994756 c = 0.416994756 Simplifying c = 0.416994756

Solution

The solution to the problem is based on the solutions from the subproblems. c = {21.583005244, 0.416994756}

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