q^2-4q=10

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Solution for q^2-4q=10 equation: 


Simplifying
q2 + -4q = 10

Reorder the terms:
-4q + q2 = 10

Solving
-4q + q2 = 10

Solving for variable 'q'.

Reorder the terms:
-10 + -4q + q2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -4q + 10 + q2 = 0 + 10

Reorder the terms:
-10 + 10 + -4q + q2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -4q + q2 = 0 + 10
-4q + q2 = 0 + 10

Combine like terms: 0 + 10 = 10
-4q + q2 = 10

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = 10 + 4

Reorder the terms:
4 + -4q + q2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + -4q + q2 = 14

Factor a perfect square on the left side:
(q + -2)(q + -2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(q + -2) equal to 3.741657387 and -3.741657387.


Subproblem 1
q + -2 = 3.741657387

Simplifying
q + -2 = 3.741657387

Reorder the terms:
-2 + q = 3.741657387

Solving
-2 + q = 3.741657387

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + q = 3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + q = 3.741657387 + 2
q = 3.741657387 + 2

Combine like terms: 3.741657387 + 2 = 5.741657387
q = 5.741657387

Simplifying
q = 5.741657387


Subproblem 2
q + -2 = -3.741657387

Simplifying
q + -2 = -3.741657387

Reorder the terms:
-2 + q = -3.741657387

Solving
-2 + q = -3.741657387

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + q = -3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + q = -3.741657387 + 2
q = -3.741657387 + 2

Combine like terms: -3.741657387 + 2 = -1.741657387
q = -1.741657387

Simplifying
q = -1.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {5.741657387, -1.741657387}

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