(2.26x+2.94)(2.26x+2.94)=9.02

Solution for (2.26x+2.94)(2.26x+2.94)=9.02 equation:

Simplifying
(2.26x + 2.94)(2.26x + 2.94) = 9.02

Reorder the terms:
(2.94 + 2.26x)(2.26x + 2.94) = 9.02

Reorder the terms:
(2.94 + 2.26x)(2.94 + 2.26x) = 9.02

Multiply (2.94 + 2.26x) * (2.94 + 2.26x)
(2.94(2.94 + 2.26x) + 2.26x * (2.94 + 2.26x)) = 9.02
((2.94 * 2.94 + 2.26x * 2.94) + 2.26x * (2.94 + 2.26x)) = 9.02
((8.6436 + 6.6444x) + 2.26x * (2.94 + 2.26x)) = 9.02
(8.6436 + 6.6444x + (2.94 * 2.26x + 2.26x * 2.26x)) = 9.02
(8.6436 + 6.6444x + (6.6444x + 5.1076x2)) = 9.02

Combine like terms: 6.6444x + 6.6444x = 13.2888x
(8.6436 + 13.2888x + 5.1076x2) = 9.02

Solving
8.6436 + 13.2888x + 5.1076x2 = 9.02

Solving for variable 'x'.

Reorder the terms:
8.6436 + -9.02 + 13.2888x + 5.1076x2 = 9.02 + -9.02

Combine like terms: 8.6436 + -9.02 = -0.3764
-0.3764 + 13.2888x + 5.1076x2 = 9.02 + -9.02

Combine like terms: 9.02 + -9.02 = 0.00
-0.3764 + 13.2888x + 5.1076x2 = 0.00

Begin completing the square.  Divide all terms by
5.1076 the coefficient of the squared term: 

Divide each side by '5.1076'.
-0.07369410291 + 2.601769912x + x2 = 0

Move the constant term to the right:

Add '0.07369410291' to each side of the equation.
-0.07369410291 + 2.601769912x + 0.07369410291 + x2 = 0 + 0.07369410291

Reorder the terms:
-0.07369410291 + 0.07369410291 + 2.601769912x + x2 = 0 + 0.07369410291

Combine like terms: -0.07369410291 + 0.07369410291 = 0.00000000000
0.00000000000 + 2.601769912x + x2 = 0 + 0.07369410291
2.601769912x + x2 = 0 + 0.07369410291

Combine like terms: 0 + 0.07369410291 = 0.07369410291
2.601769912x + x2 = 0.07369410291

The x term is 2.601769912x.  Take half its coefficient (1.300884956).
Square it (1.692301669) and add it to both sides.

Add '1.692301669' to each side of the equation.
2.601769912x + 1.692301669 + x2 = 0.07369410291 + 1.692301669

Reorder the terms:
1.692301669 + 2.601769912x + x2 = 0.07369410291 + 1.692301669

Combine like terms: 0.07369410291 + 1.692301669 = 1.76599577191
1.692301669 + 2.601769912x + x2 = 1.76599577191

Factor a perfect square on the left side:
(x + 1.300884956)(x + 1.300884956) = 1.76599577191

Calculate the square root of the right side: 1.328907736

Break this problem into two subproblems by setting 
(x + 1.300884956) equal to 1.328907736 and -1.328907736.

Subproblem 1
x + 1.300884956 = 1.328907736

Simplifying
x + 1.300884956 = 1.328907736

Reorder the terms:
1.300884956 + x = 1.328907736

Solving
1.300884956 + x = 1.328907736

Solving for variable 'x'.

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

Add '-1.300884956' to each side of the equation.
1.300884956 + -1.300884956 + x = 1.328907736 + -1.300884956

Combine like terms: 1.300884956 + -1.300884956 = 0.000000000
0.000000000 + x = 1.328907736 + -1.300884956
x = 1.328907736 + -1.300884956

Combine like terms: 1.328907736 + -1.300884956 = 0.02802278
x = 0.02802278

Simplifying
x = 0.02802278

Subproblem 2
x + 1.300884956 = -1.328907736

Simplifying
x + 1.300884956 = -1.328907736

Reorder the terms:
1.300884956 + x = -1.328907736

Solving
1.300884956 + x = -1.328907736

Solving for variable 'x'.

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

Add '-1.300884956' to each side of the equation.
1.300884956 + -1.300884956 + x = -1.328907736 + -1.300884956

Combine like terms: 1.300884956 + -1.300884956 = 0.000000000
0.000000000 + x = -1.328907736 + -1.300884956
x = -1.328907736 + -1.300884956

Combine like terms: -1.328907736 + -1.300884956 = -2.629792692
x = -2.629792692

Simplifying
x = -2.629792692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.02802278, -2.629792692}