4.9x^2-14.48x-6.9=0

Solution for 4.9x^2-14.48x-6.9=0 equation:

Simplifying
4.9x2 + -14.48x + -6.9 = 0

Reorder the terms:
-6.9 + -14.48x + 4.9x2 = 0

Solving
-6.9 + -14.48x + 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'.
-1.408163265 + -2.955102041x + x2 = 0

Move the constant term to the right:

Add '1.408163265' to each side of the equation.
-1.408163265 + -2.955102041x + 1.408163265 + x2 = 0 + 1.408163265

Reorder the terms:
-1.408163265 + 1.408163265 + -2.955102041x + x2 = 0 + 1.408163265

Combine like terms: -1.408163265 + 1.408163265 = 0.000000000
0.000000000 + -2.955102041x + x2 = 0 + 1.408163265
-2.955102041x + x2 = 0 + 1.408163265

Combine like terms: 0 + 1.408163265 = 1.408163265
-2.955102041x + x2 = 1.408163265

The x term is -2.955102041x.  Take half its coefficient (-1.477551021).
Square it (2.183157020) and add it to both sides.

Add '2.183157020' to each side of the equation.
-2.955102041x + 2.183157020 + x2 = 1.408163265 + 2.183157020

Reorder the terms:
2.183157020 + -2.955102041x + x2 = 1.408163265 + 2.183157020

Combine like terms: 1.408163265 + 2.183157020 = 3.591320285
2.183157020 + -2.955102041x + x2 = 3.591320285

Factor a perfect square on the left side:
(x + -1.477551021)(x + -1.477551021) = 3.591320285

Calculate the square root of the right side: 1.89507791

Break this problem into two subproblems by setting 
(x + -1.477551021) equal to 1.89507791 and -1.89507791.

Subproblem 1
x + -1.477551021 = 1.89507791

Simplifying
x + -1.477551021 = 1.89507791

Reorder the terms:
-1.477551021 + x = 1.89507791

Solving
-1.477551021 + x = 1.89507791

Solving for variable 'x'.

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

Add '1.477551021' to each side of the equation.
-1.477551021 + 1.477551021 + x = 1.89507791 + 1.477551021

Combine like terms: -1.477551021 + 1.477551021 = 0.000000000
0.000000000 + x = 1.89507791 + 1.477551021
x = 1.89507791 + 1.477551021

Combine like terms: 1.89507791 + 1.477551021 = 3.372628931
x = 3.372628931

Simplifying
x = 3.372628931

Subproblem 2
x + -1.477551021 = -1.89507791

Simplifying
x + -1.477551021 = -1.89507791

Reorder the terms:
-1.477551021 + x = -1.89507791

Solving
-1.477551021 + x = -1.89507791

Solving for variable 'x'.

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

Add '1.477551021' to each side of the equation.
-1.477551021 + 1.477551021 + x = -1.89507791 + 1.477551021

Combine like terms: -1.477551021 + 1.477551021 = 0.000000000
0.000000000 + x = -1.89507791 + 1.477551021
x = -1.89507791 + 1.477551021

Combine like terms: -1.89507791 + 1.477551021 = -0.417526889
x = -0.417526889

Simplifying
x = -0.417526889

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.372628931, -0.417526889}