Q^2-200Q+25=0

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Solution for Q^2-200Q+25=0 equation:


Simplifying
Q2 + -200Q + 25 = 0

Reorder the terms:
25 + -200Q + Q2 = 0

Solving
25 + -200Q + Q2 = 0

Solving for variable 'Q'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -200Q + -25 + Q2 = 0 + -25

Reorder the terms:
25 + -25 + -200Q + Q2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -200Q + Q2 = 0 + -25
-200Q + Q2 = 0 + -25

Combine like terms: 0 + -25 = -25
-200Q + Q2 = -25

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 = -25 + 10000

Reorder the terms:
10000 + -200Q + Q2 = -25 + 10000

Combine like terms: -25 + 10000 = 9975
10000 + -200Q + Q2 = 9975

Factor a perfect square on the left side:
(Q + -100)(Q + -100) = 9975

Calculate the square root of the right side: 99.874921777

Break this problem into two subproblems by setting 
(Q + -100) equal to 99.874921777 and -99.874921777.

Subproblem 1

Q + -100 = 99.874921777 Simplifying Q + -100 = 99.874921777 Reorder the terms: -100 + Q = 99.874921777 Solving -100 + Q = 99.874921777 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 = 99.874921777 + 100 Combine like terms: -100 + 100 = 0 0 + Q = 99.874921777 + 100 Q = 99.874921777 + 100 Combine like terms: 99.874921777 + 100 = 199.874921777 Q = 199.874921777 Simplifying Q = 199.874921777

Subproblem 2

Q + -100 = -99.874921777 Simplifying Q + -100 = -99.874921777 Reorder the terms: -100 + Q = -99.874921777 Solving -100 + Q = -99.874921777 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 = -99.874921777 + 100 Combine like terms: -100 + 100 = 0 0 + Q = -99.874921777 + 100 Q = -99.874921777 + 100 Combine like terms: -99.874921777 + 100 = 0.125078223 Q = 0.125078223 Simplifying Q = 0.125078223

Solution

The solution to the problem is based on the solutions from the subproblems. Q = {199.874921777, 0.125078223}

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