q^2-22q=-5

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Solution for q^2-22q=-5 equation:


Simplifying
q2 + -22q = -5

Reorder the terms:
-22q + q2 = -5

Solving
-22q + q2 = -5

Solving for variable 'q'.

Reorder the terms:
5 + -22q + q2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -22q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -22q + -5 + q2 = 0 + -5

Reorder the terms:
5 + -5 + -22q + q2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -22q + q2 = 0 + -5
-22q + q2 = 0 + -5

Combine like terms: 0 + -5 = -5
-22q + q2 = -5

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

Add '121' to each side of the equation.
-22q + 121 + q2 = -5 + 121

Reorder the terms:
121 + -22q + q2 = -5 + 121

Combine like terms: -5 + 121 = 116
121 + -22q + q2 = 116

Factor a perfect square on the left side:
(q + -11)(q + -11) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(q + -11) equal to 10.770329614 and -10.770329614.

Subproblem 1

q + -11 = 10.770329614 Simplifying q + -11 = 10.770329614 Reorder the terms: -11 + q = 10.770329614 Solving -11 + q = 10.770329614 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + q = 10.770329614 + 11 Combine like terms: -11 + 11 = 0 0 + q = 10.770329614 + 11 q = 10.770329614 + 11 Combine like terms: 10.770329614 + 11 = 21.770329614 q = 21.770329614 Simplifying q = 21.770329614

Subproblem 2

q + -11 = -10.770329614 Simplifying q + -11 = -10.770329614 Reorder the terms: -11 + q = -10.770329614 Solving -11 + q = -10.770329614 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + q = -10.770329614 + 11 Combine like terms: -11 + 11 = 0 0 + q = -10.770329614 + 11 q = -10.770329614 + 11 Combine like terms: -10.770329614 + 11 = 0.229670386 q = 0.229670386 Simplifying q = 0.229670386

Solution

The solution to the problem is based on the solutions from the subproblems. q = {21.770329614, 0.229670386}

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