10u^2-27u+8=0

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Solution for 10u^2-27u+8=0 equation:


Simplifying
10u2 + -27u + 8 = 0

Reorder the terms:
8 + -27u + 10u2 = 0

Solving
8 + -27u + 10u2 = 0

Solving for variable 'u'.

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

Divide each side by '10'.
0.8 + -2.7u + u2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.7u + -0.8 + u2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.7u + u2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.7u + u2 = 0 + -0.8
-2.7u + u2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.7u + u2 = -0.8

The u term is -2.7u.  Take half its coefficient (-1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
-2.7u + 1.8225 + u2 = -0.8 + 1.8225

Reorder the terms:
1.8225 + -2.7u + u2 = -0.8 + 1.8225

Combine like terms: -0.8 + 1.8225 = 1.0225
1.8225 + -2.7u + u2 = 1.0225

Factor a perfect square on the left side:
(u + -1.35)(u + -1.35) = 1.0225

Calculate the square root of the right side: 1.011187421

Break this problem into two subproblems by setting 
(u + -1.35) equal to 1.011187421 and -1.011187421.

Subproblem 1

u + -1.35 = 1.011187421 Simplifying u + -1.35 = 1.011187421 Reorder the terms: -1.35 + u = 1.011187421 Solving -1.35 + u = 1.011187421 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + u = 1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + u = 1.011187421 + 1.35 u = 1.011187421 + 1.35 Combine like terms: 1.011187421 + 1.35 = 2.361187421 u = 2.361187421 Simplifying u = 2.361187421

Subproblem 2

u + -1.35 = -1.011187421 Simplifying u + -1.35 = -1.011187421 Reorder the terms: -1.35 + u = -1.011187421 Solving -1.35 + u = -1.011187421 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + u = -1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + u = -1.011187421 + 1.35 u = -1.011187421 + 1.35 Combine like terms: -1.011187421 + 1.35 = 0.338812579 u = 0.338812579 Simplifying u = 0.338812579

Solution

The solution to the problem is based on the solutions from the subproblems. u = {2.361187421, 0.338812579}

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