q^2-50q+136=0

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Solution for q^2-50q+136=0 equation: 


Simplifying
q2 + -50q + 136 = 0

Reorder the terms:
136 + -50q + q2 = 0

Solving
136 + -50q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-136' to each side of the equation.
136 + -50q + -136 + q2 = 0 + -136

Reorder the terms:
136 + -136 + -50q + q2 = 0 + -136

Combine like terms: 136 + -136 = 0
0 + -50q + q2 = 0 + -136
-50q + q2 = 0 + -136

Combine like terms: 0 + -136 = -136
-50q + q2 = -136

The q term is -50q.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50q + 625 + q2 = -136 + 625

Reorder the terms:
625 + -50q + q2 = -136 + 625

Combine like terms: -136 + 625 = 489
625 + -50q + q2 = 489

Factor a perfect square on the left side:
(q + -25)(q + -25) = 489

Calculate the square root of the right side: 22.113344387

Break this problem into two subproblems by setting 
(q + -25) equal to 22.113344387 and -22.113344387.


Subproblem 1
q + -25 = 22.113344387

Simplifying
q + -25 = 22.113344387

Reorder the terms:
-25 + q = 22.113344387

Solving
-25 + q = 22.113344387

Solving for variable 'q'.

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

Add '25' to each side of the equation.
-25 + 25 + q = 22.113344387 + 25

Combine like terms: -25 + 25 = 0
0 + q = 22.113344387 + 25
q = 22.113344387 + 25

Combine like terms: 22.113344387 + 25 = 47.113344387
q = 47.113344387

Simplifying
q = 47.113344387


Subproblem 2
q + -25 = -22.113344387

Simplifying
q + -25 = -22.113344387

Reorder the terms:
-25 + q = -22.113344387

Solving
-25 + q = -22.113344387

Solving for variable 'q'.

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

Add '25' to each side of the equation.
-25 + 25 + q = -22.113344387 + 25

Combine like terms: -25 + 25 = 0
0 + q = -22.113344387 + 25
q = -22.113344387 + 25

Combine like terms: -22.113344387 + 25 = 2.886655613
q = 2.886655613

Simplifying
q = 2.886655613


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {47.113344387, 2.886655613}

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