q+q^2=14

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Solution for q+q^2=14 equation:


Simplifying
q + q2 = 14

Solving
q + q2 = 14

Solving for variable 'q'.

Reorder the terms:
-14 + q + q2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + q + 14 + q2 = 0 + 14

Reorder the terms:
-14 + 14 + q + q2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + q + q2 = 0 + 14
q + q2 = 0 + 14

Combine like terms: 0 + 14 = 14
q + q2 = 14

The q term is q.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
q + 0.25 + q2 = 14 + 0.25

Reorder the terms:
0.25 + q + q2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + q + q2 = 14.25

Factor a perfect square on the left side:
(q + 0.5)(q + 0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(q + 0.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

q + 0.5 = 3.774917218 Simplifying q + 0.5 = 3.774917218 Reorder the terms: 0.5 + q = 3.774917218 Solving 0.5 + q = 3.774917218 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 3.774917218 + -0.5 q = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 q = 3.274917218 Simplifying q = 3.274917218

Subproblem 2

q + 0.5 = -3.774917218 Simplifying q + 0.5 = -3.774917218 Reorder the terms: 0.5 + q = -3.774917218 Solving 0.5 + q = -3.774917218 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -3.774917218 + -0.5 q = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 q = -4.274917218 Simplifying q = -4.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. q = {3.274917218, -4.274917218}

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