q^2-200q+5400=0

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Solution for q^2-200q+5400=0 equation:


Simplifying
q2 + -200q + 5400 = 0

Reorder the terms:
5400 + -200q + q2 = 0

Solving
5400 + -200q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-5400' to each side of the equation.
5400 + -200q + -5400 + q2 = 0 + -5400

Reorder the terms:
5400 + -5400 + -200q + q2 = 0 + -5400

Combine like terms: 5400 + -5400 = 0
0 + -200q + q2 = 0 + -5400
-200q + q2 = 0 + -5400

Combine like terms: 0 + -5400 = -5400
-200q + q2 = -5400

The q term is -200q.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200q + 10000 + q2 = -5400 + 10000

Reorder the terms:
10000 + -200q + q2 = -5400 + 10000

Combine like terms: -5400 + 10000 = 4600
10000 + -200q + q2 = 4600

Factor a perfect square on the left side:
(q + -100)(q + -100) = 4600

Calculate the square root of the right side: 67.823299831

Break this problem into two subproblems by setting 
(q + -100) equal to 67.823299831 and -67.823299831.

Subproblem 1

q + -100 = 67.823299831 Simplifying q + -100 = 67.823299831 Reorder the terms: -100 + q = 67.823299831 Solving -100 + q = 67.823299831 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + q = 67.823299831 + 100 Combine like terms: -100 + 100 = 0 0 + q = 67.823299831 + 100 q = 67.823299831 + 100 Combine like terms: 67.823299831 + 100 = 167.823299831 q = 167.823299831 Simplifying q = 167.823299831

Subproblem 2

q + -100 = -67.823299831 Simplifying q + -100 = -67.823299831 Reorder the terms: -100 + q = -67.823299831 Solving -100 + q = -67.823299831 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + q = -67.823299831 + 100 Combine like terms: -100 + 100 = 0 0 + q = -67.823299831 + 100 q = -67.823299831 + 100 Combine like terms: -67.823299831 + 100 = 32.176700169 q = 32.176700169 Simplifying q = 32.176700169

Solution

The solution to the problem is based on the solutions from the subproblems. q = {167.823299831, 32.176700169}

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