-49x^2+43.4x+6.3=0

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Solution for -49x^2+43.4x+6.3=0 equation: 


Simplifying
-49x2 + 43.4x + 6.3 = 0

Reorder the terms:
6.3 + 43.4x + -49x2 = 0

Solving
6.3 + 43.4x + -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'.
-0.1285714286 + -0.8857142857x + x2 = 0

Move the constant term to the right:

Add '0.1285714286' to each side of the equation.
-0.1285714286 + -0.8857142857x + 0.1285714286 + x2 = 0 + 0.1285714286

Reorder the terms:
-0.1285714286 + 0.1285714286 + -0.8857142857x + x2 = 0 + 0.1285714286

Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000
0.0000000000 + -0.8857142857x + x2 = 0 + 0.1285714286
-0.8857142857x + x2 = 0 + 0.1285714286

Combine like terms: 0 + 0.1285714286 = 0.1285714286
-0.8857142857x + x2 = 0.1285714286

The x term is -0.8857142857x.  Take half its coefficient (-0.4428571429).
Square it (0.1961224490) and add it to both sides.

Add '0.1961224490' to each side of the equation.
-0.8857142857x + 0.1961224490 + x2 = 0.1285714286 + 0.1961224490

Reorder the terms:
0.1961224490 + -0.8857142857x + x2 = 0.1285714286 + 0.1961224490

Combine like terms: 0.1285714286 + 0.1961224490 = 0.3246938776
0.1961224490 + -0.8857142857x + x2 = 0.3246938776

Factor a perfect square on the left side:
(x + -0.4428571429)(x + -0.4428571429) = 0.3246938776

Calculate the square root of the right side: 0.569819162

Break this problem into two subproblems by setting 
(x + -0.4428571429) equal to 0.569819162 and -0.569819162.


Subproblem 1
x + -0.4428571429 = 0.569819162

Simplifying
x + -0.4428571429 = 0.569819162

Reorder the terms:
-0.4428571429 + x = 0.569819162

Solving
-0.4428571429 + x = 0.569819162

Solving for variable 'x'.

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

Add '0.4428571429' to each side of the equation.
-0.4428571429 + 0.4428571429 + x = 0.569819162 + 0.4428571429

Combine like terms: -0.4428571429 + 0.4428571429 = 0.0000000000
0.0000000000 + x = 0.569819162 + 0.4428571429
x = 0.569819162 + 0.4428571429

Combine like terms: 0.569819162 + 0.4428571429 = 1.0126763049
x = 1.0126763049

Simplifying
x = 1.0126763049


Subproblem 2
x + -0.4428571429 = -0.569819162

Simplifying
x + -0.4428571429 = -0.569819162

Reorder the terms:
-0.4428571429 + x = -0.569819162

Solving
-0.4428571429 + x = -0.569819162

Solving for variable 'x'.

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

Add '0.4428571429' to each side of the equation.
-0.4428571429 + 0.4428571429 + x = -0.569819162 + 0.4428571429

Combine like terms: -0.4428571429 + 0.4428571429 = 0.0000000000
0.0000000000 + x = -0.569819162 + 0.4428571429
x = -0.569819162 + 0.4428571429

Combine like terms: -0.569819162 + 0.4428571429 = -0.1269620191
x = -0.1269620191

Simplifying
x = -0.1269620191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0126763049, -0.1269620191}

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