q^2+22q=25

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Solution for q^2+22q=25 equation:


Simplifying
q2 + 22q = 25

Reorder the terms:
22q + q2 = 25

Solving
22q + q2 = 25

Solving for variable 'q'.

Reorder the terms:
-25 + 22q + q2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 22q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 22q + 25 + q2 = 0 + 25

Reorder the terms:
-25 + 25 + 22q + q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 22q + q2 = 0 + 25
22q + q2 = 0 + 25

Combine like terms: 0 + 25 = 25
22q + q2 = 25

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 = 25 + 121

Reorder the terms:
121 + 22q + q2 = 25 + 121

Combine like terms: 25 + 121 = 146
121 + 22q + q2 = 146

Factor a perfect square on the left side:
(q + 11)(q + 11) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(q + 11) equal to 12.083045974 and -12.083045974.

Subproblem 1

q + 11 = 12.083045974 Simplifying q + 11 = 12.083045974 Reorder the terms: 11 + q = 12.083045974 Solving 11 + q = 12.083045974 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 = 12.083045974 + -11 Combine like terms: 11 + -11 = 0 0 + q = 12.083045974 + -11 q = 12.083045974 + -11 Combine like terms: 12.083045974 + -11 = 1.083045974 q = 1.083045974 Simplifying q = 1.083045974

Subproblem 2

q + 11 = -12.083045974 Simplifying q + 11 = -12.083045974 Reorder the terms: 11 + q = -12.083045974 Solving 11 + q = -12.083045974 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 = -12.083045974 + -11 Combine like terms: 11 + -11 = 0 0 + q = -12.083045974 + -11 q = -12.083045974 + -11 Combine like terms: -12.083045974 + -11 = -23.083045974 q = -23.083045974 Simplifying q = -23.083045974

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.083045974, -23.083045974}

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