7.61x^2+2.79x=5.33

Solution for 7.61x^2+2.79x=5.33 equation:

Simplifying
7.61x2 + 2.79x = 5.33

Reorder the terms:
2.79x + 7.61x2 = 5.33

Solving
2.79x + 7.61x2 = 5.33

Solving for variable 'x'.

Reorder the terms:
-5.33 + 2.79x + 7.61x2 = 5.33 + -5.33

Combine like terms: 5.33 + -5.33 = 0.00
-5.33 + 2.79x + 7.61x2 = 0.00

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

Divide each side by '7.61'.
-0.7003942181 + 0.3666228647x + x2 = 0

Move the constant term to the right:

Add '0.7003942181' to each side of the equation.
-0.7003942181 + 0.3666228647x + 0.7003942181 + x2 = 0 + 0.7003942181

Reorder the terms:
-0.7003942181 + 0.7003942181 + 0.3666228647x + x2 = 0 + 0.7003942181

Combine like terms: -0.7003942181 + 0.7003942181 = 0.0000000000
0.0000000000 + 0.3666228647x + x2 = 0 + 0.7003942181
0.3666228647x + x2 = 0 + 0.7003942181

Combine like terms: 0 + 0.7003942181 = 0.7003942181
0.3666228647x + x2 = 0.7003942181

The x term is 0.3666228647x.  Take half its coefficient (0.1833114324).
Square it (0.03360308125) and add it to both sides.

Add '0.03360308125' to each side of the equation.
0.3666228647x + 0.03360308125 + x2 = 0.7003942181 + 0.03360308125

Reorder the terms:
0.03360308125 + 0.3666228647x + x2 = 0.7003942181 + 0.03360308125

Combine like terms: 0.7003942181 + 0.03360308125 = 0.73399729935
0.03360308125 + 0.3666228647x + x2 = 0.73399729935

Factor a perfect square on the left side:
(x + 0.1833114324)(x + 0.1833114324) = 0.73399729935

Calculate the square root of the right side: 0.856736423

Break this problem into two subproblems by setting 
(x + 0.1833114324) equal to 0.856736423 and -0.856736423.

Subproblem 1
x + 0.1833114324 = 0.856736423

Simplifying
x + 0.1833114324 = 0.856736423

Reorder the terms:
0.1833114324 + x = 0.856736423

Solving
0.1833114324 + x = 0.856736423

Solving for variable 'x'.

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

Add '-0.1833114324' to each side of the equation.
0.1833114324 + -0.1833114324 + x = 0.856736423 + -0.1833114324

Combine like terms: 0.1833114324 + -0.1833114324 = 0.0000000000
0.0000000000 + x = 0.856736423 + -0.1833114324
x = 0.856736423 + -0.1833114324

Combine like terms: 0.856736423 + -0.1833114324 = 0.6734249906
x = 0.6734249906

Simplifying
x = 0.6734249906

Subproblem 2
x + 0.1833114324 = -0.856736423

Simplifying
x + 0.1833114324 = -0.856736423

Reorder the terms:
0.1833114324 + x = -0.856736423

Solving
0.1833114324 + x = -0.856736423

Solving for variable 'x'.

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

Add '-0.1833114324' to each side of the equation.
0.1833114324 + -0.1833114324 + x = -0.856736423 + -0.1833114324

Combine like terms: 0.1833114324 + -0.1833114324 = 0.0000000000
0.0000000000 + x = -0.856736423 + -0.1833114324
x = -0.856736423 + -0.1833114324

Combine like terms: -0.856736423 + -0.1833114324 = -1.0400478554
x = -1.0400478554

Simplifying
x = -1.0400478554

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6734249906, -1.0400478554}