49x^2-98x+43=0

Solution for 49x^2-98x+43=0 equation:

Simplifying
49x2 + -98x + 43 = 0

Reorder the terms:
43 + -98x + 49x2 = 0

Solving
43 + -98x + 49x2 = 0

Solving for variable 'x'.

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

Divide each side by '49'.
0.8775510204 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.8775510204' to each side of the equation.
0.8775510204 + -2x + -0.8775510204 + x2 = 0 + -0.8775510204

Reorder the terms:
0.8775510204 + -0.8775510204 + -2x + x2 = 0 + -0.8775510204

Combine like terms: 0.8775510204 + -0.8775510204 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.8775510204
-2x + x2 = 0 + -0.8775510204

Combine like terms: 0 + -0.8775510204 = -0.8775510204
-2x + x2 = -0.8775510204

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.8775510204 + 1

Reorder the terms:
1 + -2x + x2 = -0.8775510204 + 1

Combine like terms: -0.8775510204 + 1 = 0.1224489796
1 + -2x + x2 = 0.1224489796

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.1224489796

Calculate the square root of the right side: 0.349927106

Break this problem into two subproblems by setting 
(x + -1) equal to 0.349927106 and -0.349927106.

Subproblem 1
x + -1 = 0.349927106

Simplifying
x + -1 = 0.349927106

Reorder the terms:
-1 + x = 0.349927106

Solving
-1 + x = 0.349927106

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.349927106 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.349927106 + 1
x = 0.349927106 + 1

Combine like terms: 0.349927106 + 1 = 1.349927106
x = 1.349927106

Simplifying
x = 1.349927106

Subproblem 2
x + -1 = -0.349927106

Simplifying
x + -1 = -0.349927106

Reorder the terms:
-1 + x = -0.349927106

Solving
-1 + x = -0.349927106

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.349927106 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.349927106 + 1
x = -0.349927106 + 1

Combine like terms: -0.349927106 + 1 = 0.650072894
x = 0.650072894

Simplifying
x = 0.650072894

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.349927106, 0.650072894}