-4.9x^2+43.4x+6.3=0

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Solution for -4.9x^2+43.4x+6.3=0 equation: 


Simplifying
-4.9x2 + 43.4x + 6.3 = 0

Reorder the terms:
6.3 + 43.4x + -4.9x2 = 0

Solving
6.3 + 43.4x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-1.285714286 + -8.857142857x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -8.857142857x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -8.857142857x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -8.857142857x + x2 = 0 + 1.285714286
-8.857142857x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-8.857142857x + x2 = 1.285714286

The x term is -8.857142857x.  Take half its coefficient (-4.428571429).
Square it (19.61224490) and add it to both sides.

Add '19.61224490' to each side of the equation.
-8.857142857x + 19.61224490 + x2 = 1.285714286 + 19.61224490

Reorder the terms:
19.61224490 + -8.857142857x + x2 = 1.285714286 + 19.61224490

Combine like terms: 1.285714286 + 19.61224490 = 20.897959186
19.61224490 + -8.857142857x + x2 = 20.897959186

Factor a perfect square on the left side:
(x + -4.428571429)(x + -4.428571429) = 20.897959186

Calculate the square root of the right side: 4.571428572

Break this problem into two subproblems by setting 
(x + -4.428571429) equal to 4.571428572 and -4.571428572.


Subproblem 1
x + -4.428571429 = 4.571428572

Simplifying
x + -4.428571429 = 4.571428572

Reorder the terms:
-4.428571429 + x = 4.571428572

Solving
-4.428571429 + x = 4.571428572

Solving for variable 'x'.

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

Add '4.428571429' to each side of the equation.
-4.428571429 + 4.428571429 + x = 4.571428572 + 4.428571429

Combine like terms: -4.428571429 + 4.428571429 = 0.000000000
0.000000000 + x = 4.571428572 + 4.428571429
x = 4.571428572 + 4.428571429

Combine like terms: 4.571428572 + 4.428571429 = 9.000000001
x = 9.000000001

Simplifying
x = 9.000000001


Subproblem 2
x + -4.428571429 = -4.571428572

Simplifying
x + -4.428571429 = -4.571428572

Reorder the terms:
-4.428571429 + x = -4.571428572

Solving
-4.428571429 + x = -4.571428572

Solving for variable 'x'.

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

Add '4.428571429' to each side of the equation.
-4.428571429 + 4.428571429 + x = -4.571428572 + 4.428571429

Combine like terms: -4.428571429 + 4.428571429 = 0.000000000
0.000000000 + x = -4.571428572 + 4.428571429
x = -4.571428572 + 4.428571429

Combine like terms: -4.571428572 + 4.428571429 = -0.142857143
x = -0.142857143

Simplifying
x = -0.142857143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.000000001, -0.142857143}

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