7.53x^2+2.81x=4.75

Solution for 7.53x^2+2.81x=4.75 equation:

Simplifying
7.53x2 + 2.81x = 4.75

Reorder the terms:
2.81x + 7.53x2 = 4.75

Solving
2.81x + 7.53x2 = 4.75

Solving for variable 'x'.

Reorder the terms:
-4.75 + 2.81x + 7.53x2 = 4.75 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
-4.75 + 2.81x + 7.53x2 = 0.00

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

Divide each side by '7.53'.
-0.630810093 + 0.3731739708x + x2 = 0

Move the constant term to the right:

Add '0.630810093' to each side of the equation.
-0.630810093 + 0.3731739708x + 0.630810093 + x2 = 0 + 0.630810093

Reorder the terms:
-0.630810093 + 0.630810093 + 0.3731739708x + x2 = 0 + 0.630810093

Combine like terms: -0.630810093 + 0.630810093 = 0.000000000
0.000000000 + 0.3731739708x + x2 = 0 + 0.630810093
0.3731739708x + x2 = 0 + 0.630810093

Combine like terms: 0 + 0.630810093 = 0.630810093
0.3731739708x + x2 = 0.630810093

The x term is 0.3731739708x.  Take half its coefficient (0.1865869854).
Square it (0.03481470312) and add it to both sides.

Add '0.03481470312' to each side of the equation.
0.3731739708x + 0.03481470312 + x2 = 0.630810093 + 0.03481470312

Reorder the terms:
0.03481470312 + 0.3731739708x + x2 = 0.630810093 + 0.03481470312

Combine like terms: 0.630810093 + 0.03481470312 = 0.66562479612
0.03481470312 + 0.3731739708x + x2 = 0.66562479612

Factor a perfect square on the left side:
(x + 0.1865869854)(x + 0.1865869854) = 0.66562479612

Calculate the square root of the right side: 0.815858319

Break this problem into two subproblems by setting 
(x + 0.1865869854) equal to 0.815858319 and -0.815858319.

Subproblem 1
x + 0.1865869854 = 0.815858319

Simplifying
x + 0.1865869854 = 0.815858319

Reorder the terms:
0.1865869854 + x = 0.815858319

Solving
0.1865869854 + x = 0.815858319

Solving for variable 'x'.

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

Add '-0.1865869854' to each side of the equation.
0.1865869854 + -0.1865869854 + x = 0.815858319 + -0.1865869854

Combine like terms: 0.1865869854 + -0.1865869854 = 0.0000000000
0.0000000000 + x = 0.815858319 + -0.1865869854
x = 0.815858319 + -0.1865869854

Combine like terms: 0.815858319 + -0.1865869854 = 0.6292713336
x = 0.6292713336

Simplifying
x = 0.6292713336

Subproblem 2
x + 0.1865869854 = -0.815858319

Simplifying
x + 0.1865869854 = -0.815858319

Reorder the terms:
0.1865869854 + x = -0.815858319

Solving
0.1865869854 + x = -0.815858319

Solving for variable 'x'.

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

Add '-0.1865869854' to each side of the equation.
0.1865869854 + -0.1865869854 + x = -0.815858319 + -0.1865869854

Combine like terms: 0.1865869854 + -0.1865869854 = 0.0000000000
0.0000000000 + x = -0.815858319 + -0.1865869854
x = -0.815858319 + -0.1865869854

Combine like terms: -0.815858319 + -0.1865869854 = -1.0024453044
x = -1.0024453044

Simplifying
x = -1.0024453044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6292713336, -1.0024453044}