5x^2-11x=2x+3

Solution for 5x^2-11x=2x+3 equation:

Simplifying
5x2 + -11x = 2x + 3

Reorder the terms:
-11x + 5x2 = 2x + 3

Reorder the terms:
-11x + 5x2 = 3 + 2x

Solving
-11x + 5x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + -11x + -2x + 5x2 = 3 + 2x + -3 + -2x

Combine like terms: -11x + -2x = -13x
-3 + -13x + 5x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-3 + -13x + 5x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-3 + -13x + 5x2 = 0 + 2x + -2x
-3 + -13x + 5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + -13x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -2.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.6x + x2 = 0 + 0.6
-2.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.6x + x2 = 0.6

The x term is -2.6x.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6x + 1.69 + x2 = 0.6 + 1.69

Reorder the terms:
1.69 + -2.6x + x2 = 0.6 + 1.69

Combine like terms: 0.6 + 1.69 = 2.29
1.69 + -2.6x + x2 = 2.29

Factor a perfect square on the left side:
(x + -1.3)(x + -1.3) = 2.29

Calculate the square root of the right side: 1.513274595

Break this problem into two subproblems by setting 
(x + -1.3) equal to 1.513274595 and -1.513274595.

Subproblem 1
x + -1.3 = 1.513274595

Simplifying
x + -1.3 = 1.513274595

Reorder the terms:
-1.3 + x = 1.513274595

Solving
-1.3 + x = 1.513274595

Solving for variable 'x'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + x = 1.513274595 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + x = 1.513274595 + 1.3
x = 1.513274595 + 1.3

Combine like terms: 1.513274595 + 1.3 = 2.813274595
x = 2.813274595

Simplifying
x = 2.813274595

Subproblem 2
x + -1.3 = -1.513274595

Simplifying
x + -1.3 = -1.513274595

Reorder the terms:
-1.3 + x = -1.513274595

Solving
-1.3 + x = -1.513274595

Solving for variable 'x'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + x = -1.513274595 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + x = -1.513274595 + 1.3
x = -1.513274595 + 1.3

Combine like terms: -1.513274595 + 1.3 = -0.213274595
x = -0.213274595

Simplifying
x = -0.213274595

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.813274595, -0.213274595}