10000+q^2=220q

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Solution for 10000+q^2=220q equation:


Simplifying
10000 + q2 = 220q

Solving
10000 + q2 = 220q

Solving for variable 'q'.

Reorder the terms:
10000 + -220q + q2 = 220q + -220q

Combine like terms: 220q + -220q = 0
10000 + -220q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10000' to each side of the equation.
10000 + -220q + -10000 + q2 = 0 + -10000

Reorder the terms:
10000 + -10000 + -220q + q2 = 0 + -10000

Combine like terms: 10000 + -10000 = 0
0 + -220q + q2 = 0 + -10000
-220q + q2 = 0 + -10000

Combine like terms: 0 + -10000 = -10000
-220q + q2 = -10000

The q term is -220q.  Take half its coefficient (-110).
Square it (12100) and add it to both sides.

Add '12100' to each side of the equation.
-220q + 12100 + q2 = -10000 + 12100

Reorder the terms:
12100 + -220q + q2 = -10000 + 12100

Combine like terms: -10000 + 12100 = 2100
12100 + -220q + q2 = 2100

Factor a perfect square on the left side:
(q + -110)(q + -110) = 2100

Calculate the square root of the right side: 45.82575695

Break this problem into two subproblems by setting 
(q + -110) equal to 45.82575695 and -45.82575695.

Subproblem 1

q + -110 = 45.82575695 Simplifying q + -110 = 45.82575695 Reorder the terms: -110 + q = 45.82575695 Solving -110 + q = 45.82575695 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + q = 45.82575695 + 110 Combine like terms: -110 + 110 = 0 0 + q = 45.82575695 + 110 q = 45.82575695 + 110 Combine like terms: 45.82575695 + 110 = 155.82575695 q = 155.82575695 Simplifying q = 155.82575695

Subproblem 2

q + -110 = -45.82575695 Simplifying q + -110 = -45.82575695 Reorder the terms: -110 + q = -45.82575695 Solving -110 + q = -45.82575695 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + q = -45.82575695 + 110 Combine like terms: -110 + 110 = 0 0 + q = -45.82575695 + 110 q = -45.82575695 + 110 Combine like terms: -45.82575695 + 110 = 64.17424305 q = 64.17424305 Simplifying q = 64.17424305

Solution

The solution to the problem is based on the solutions from the subproblems. q = {155.82575695, 64.17424305}

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