47.1x^2=.0289-4x^2-.34x

Solution for 47.1x^2=.0289-4x^2-.34x equation:

Simplifying
47.1x2 = 0.0289 + -4x2 + -0.34x

Reorder the terms:
47.1x2 = 0.0289 + -0.34x + -4x2

Solving
47.1x2 = 0.0289 + -0.34x + -4x2

Solving for variable 'x'.

Reorder the terms:
-0.0289 + 0.34x + 47.1x2 + 4x2 = 0.0289 + -0.34x + -4x2 + -0.0289 + 0.34x + 4x2

Combine like terms: 47.1x2 + 4x2 = 51.1x2
-0.0289 + 0.34x + 51.1x2 = 0.0289 + -0.34x + -4x2 + -0.0289 + 0.34x + 4x2

Reorder the terms:
-0.0289 + 0.34x + 51.1x2 = 0.0289 + -0.0289 + -0.34x + 0.34x + -4x2 + 4x2

Combine like terms: 0.0289 + -0.0289 = 0.0000
-0.0289 + 0.34x + 51.1x2 = 0.0000 + -0.34x + 0.34x + -4x2 + 4x2
-0.0289 + 0.34x + 51.1x2 = -0.34x + 0.34x + -4x2 + 4x2

Combine like terms: -0.34x + 0.34x = 0.00
-0.0289 + 0.34x + 51.1x2 = 0.00 + -4x2 + 4x2
-0.0289 + 0.34x + 51.1x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-0.0289 + 0.34x + 51.1x2 = 0

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

Divide each side by '51.1'.
-0.0005655577299 + 0.006653620352x + x2 = 0

Move the constant term to the right:

Add '0.0005655577299' to each side of the equation.
-0.0005655577299 + 0.006653620352x + 0.0005655577299 + x2 = 0 + 0.0005655577299

Reorder the terms:
-0.0005655577299 + 0.0005655577299 + 0.006653620352x + x2 = 0 + 0.0005655577299

Combine like terms: -0.0005655577299 + 0.0005655577299 = 0.0000000000000
0.0000000000000 + 0.006653620352x + x2 = 0 + 0.0005655577299
0.006653620352x + x2 = 0 + 0.0005655577299

Combine like terms: 0 + 0.0005655577299 = 0.0005655577299
0.006653620352x + x2 = 0.0005655577299

The x term is 0.006653620352x.  Take half its coefficient (0.003326810176).
Square it (0.00001106766595) and add it to both sides.

Add '0.00001106766595' to each side of the equation.
0.006653620352x + 0.00001106766595 + x2 = 0.0005655577299 + 0.00001106766595

Reorder the terms:
0.00001106766595 + 0.006653620352x + x2 = 0.0005655577299 + 0.00001106766595

Combine like terms: 0.0005655577299 + 0.00001106766595 = 0.00057662539585
0.00001106766595 + 0.006653620352x + x2 = 0.00057662539585

Factor a perfect square on the left side:
(x + 0.003326810176)(x + 0.003326810176) = 0.00057662539585

Calculate the square root of the right side: 0.024013026

Break this problem into two subproblems by setting 
(x + 0.003326810176) equal to 0.024013026 and -0.024013026.

Subproblem 1
x + 0.003326810176 = 0.024013026

Simplifying
x + 0.003326810176 = 0.024013026

Reorder the terms:
0.003326810176 + x = 0.024013026

Solving
0.003326810176 + x = 0.024013026

Solving for variable 'x'.

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

Add '-0.003326810176' to each side of the equation.
0.003326810176 + -0.003326810176 + x = 0.024013026 + -0.003326810176

Combine like terms: 0.003326810176 + -0.003326810176 = 0.000000000000
0.000000000000 + x = 0.024013026 + -0.003326810176
x = 0.024013026 + -0.003326810176

Combine like terms: 0.024013026 + -0.003326810176 = 0.020686215824
x = 0.020686215824

Simplifying
x = 0.020686215824

Subproblem 2
x + 0.003326810176 = -0.024013026

Simplifying
x + 0.003326810176 = -0.024013026

Reorder the terms:
0.003326810176 + x = -0.024013026

Solving
0.003326810176 + x = -0.024013026

Solving for variable 'x'.

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

Add '-0.003326810176' to each side of the equation.
0.003326810176 + -0.003326810176 + x = -0.024013026 + -0.003326810176

Combine like terms: 0.003326810176 + -0.003326810176 = 0.000000000000
0.000000000000 + x = -0.024013026 + -0.003326810176
x = -0.024013026 + -0.003326810176

Combine like terms: -0.024013026 + -0.003326810176 = -0.027339836176
x = -0.027339836176

Simplifying
x = -0.027339836176

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.020686215824, -0.027339836176}