4.9x^2-40x-120=0

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Solution for 4.9x^2-40x-120=0 equation: 


Simplifying
4.9x2 + -40x + -120 = 0

Reorder the terms:
-120 + -40x + 4.9x2 = 0

Solving
-120 + -40x + 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'.
-24.48979592 + -8.163265306x + x2 = 0

Move the constant term to the right:

Add '24.48979592' to each side of the equation.
-24.48979592 + -8.163265306x + 24.48979592 + x2 = 0 + 24.48979592

Reorder the terms:
-24.48979592 + 24.48979592 + -8.163265306x + x2 = 0 + 24.48979592

Combine like terms: -24.48979592 + 24.48979592 = 0.00000000
0.00000000 + -8.163265306x + x2 = 0 + 24.48979592
-8.163265306x + x2 = 0 + 24.48979592

Combine like terms: 0 + 24.48979592 = 24.48979592
-8.163265306x + x2 = 24.48979592

The x term is -8.163265306x.  Take half its coefficient (-4.081632653).
Square it (16.65972511) and add it to both sides.

Add '16.65972511' to each side of the equation.
-8.163265306x + 16.65972511 + x2 = 24.48979592 + 16.65972511

Reorder the terms:
16.65972511 + -8.163265306x + x2 = 24.48979592 + 16.65972511

Combine like terms: 24.48979592 + 16.65972511 = 41.14952103
16.65972511 + -8.163265306x + x2 = 41.14952103

Factor a perfect square on the left side:
(x + -4.081632653)(x + -4.081632653) = 41.14952103

Calculate the square root of the right side: 6.414789243

Break this problem into two subproblems by setting 
(x + -4.081632653) equal to 6.414789243 and -6.414789243.


Subproblem 1
x + -4.081632653 = 6.414789243

Simplifying
x + -4.081632653 = 6.414789243

Reorder the terms:
-4.081632653 + x = 6.414789243

Solving
-4.081632653 + x = 6.414789243

Solving for variable 'x'.

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

Add '4.081632653' to each side of the equation.
-4.081632653 + 4.081632653 + x = 6.414789243 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + x = 6.414789243 + 4.081632653
x = 6.414789243 + 4.081632653

Combine like terms: 6.414789243 + 4.081632653 = 10.496421896
x = 10.496421896

Simplifying
x = 10.496421896


Subproblem 2
x + -4.081632653 = -6.414789243

Simplifying
x + -4.081632653 = -6.414789243

Reorder the terms:
-4.081632653 + x = -6.414789243

Solving
-4.081632653 + x = -6.414789243

Solving for variable 'x'.

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

Add '4.081632653' to each side of the equation.
-4.081632653 + 4.081632653 + x = -6.414789243 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + x = -6.414789243 + 4.081632653
x = -6.414789243 + 4.081632653

Combine like terms: -6.414789243 + 4.081632653 = -2.33315659
x = -2.33315659

Simplifying
x = -2.33315659


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.496421896, -2.33315659}

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