0.8Q^2-1.4Q+0.5=0

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Solution for 0.8Q^2-1.4Q+0.5=0 equation:


Simplifying
0.8Q2 + -1.4Q + 0.5 = 0

Reorder the terms:
0.5 + -1.4Q + 0.8Q2 = 0

Solving
0.5 + -1.4Q + 0.8Q2 = 0

Solving for variable 'Q'.

Begin completing the square.  Divide all terms by
0.8 the coefficient of the squared term: 

Divide each side by '0.8'.
0.625 + -1.75Q + Q2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -1.75Q + -0.625 + Q2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -1.75Q + Q2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -1.75Q + Q2 = 0 + -0.625
-1.75Q + Q2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-1.75Q + Q2 = -0.625

The Q term is -1.75Q.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75Q + 0.765625 + Q2 = -0.625 + 0.765625

Reorder the terms:
0.765625 + -1.75Q + Q2 = -0.625 + 0.765625

Combine like terms: -0.625 + 0.765625 = 0.140625
0.765625 + -1.75Q + Q2 = 0.140625

Factor a perfect square on the left side:
(Q + -0.875)(Q + -0.875) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(Q + -0.875) equal to 0.375 and -0.375.


Subproblem 1
Q + -0.875 = 0.375

Simplifying
Q + -0.875 = 0.375

Reorder the terms:
-0.875 + Q = 0.375

Solving
-0.875 + Q = 0.375

Solving for variable 'Q'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + Q = 0.375 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + Q = 0.375 + 0.875
Q = 0.375 + 0.875

Combine like terms: 0.375 + 0.875 = 1.25
Q = 1.25

Simplifying
Q = 1.25


Subproblem 2
Q + -0.875 = -0.375

Simplifying
Q + -0.875 = -0.375

Reorder the terms:
-0.875 + Q = -0.375

Solving
-0.875 + Q = -0.375

Solving for variable 'Q'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + Q = -0.375 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + Q = -0.375 + 0.875
Q = -0.375 + 0.875

Combine like terms: -0.375 + 0.875 = 0.5
Q = 0.5

Simplifying
Q = 0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {1.25, 0.5}

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