4.9x^2-70x-200=0

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Solution for 4.9x^2-70x-200=0 equation: 


Simplifying
4.9x2 + -70x + -200 = 0

Reorder the terms:
-200 + -70x + 4.9x2 = 0

Solving
-200 + -70x + 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'.
-40.81632653 + -14.28571429x + x2 = 0

Move the constant term to the right:

Add '40.81632653' to each side of the equation.
-40.81632653 + -14.28571429x + 40.81632653 + x2 = 0 + 40.81632653

Reorder the terms:
-40.81632653 + 40.81632653 + -14.28571429x + x2 = 0 + 40.81632653

Combine like terms: -40.81632653 + 40.81632653 = 0.00000000
0.00000000 + -14.28571429x + x2 = 0 + 40.81632653
-14.28571429x + x2 = 0 + 40.81632653

Combine like terms: 0 + 40.81632653 = 40.81632653
-14.28571429x + x2 = 40.81632653

The x term is -14.28571429x.  Take half its coefficient (-7.142857145).
Square it (51.02040819) and add it to both sides.

Add '51.02040819' to each side of the equation.
-14.28571429x + 51.02040819 + x2 = 40.81632653 + 51.02040819

Reorder the terms:
51.02040819 + -14.28571429x + x2 = 40.81632653 + 51.02040819

Combine like terms: 40.81632653 + 51.02040819 = 91.83673472
51.02040819 + -14.28571429x + x2 = 91.83673472

Factor a perfect square on the left side:
(x + -7.142857145)(x + -7.142857145) = 91.83673472

Calculate the square root of the right side: 9.583148476

Break this problem into two subproblems by setting 
(x + -7.142857145) equal to 9.583148476 and -9.583148476.


Subproblem 1
x + -7.142857145 = 9.583148476

Simplifying
x + -7.142857145 = 9.583148476

Reorder the terms:
-7.142857145 + x = 9.583148476

Solving
-7.142857145 + x = 9.583148476

Solving for variable 'x'.

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

Add '7.142857145' to each side of the equation.
-7.142857145 + 7.142857145 + x = 9.583148476 + 7.142857145

Combine like terms: -7.142857145 + 7.142857145 = 0.000000000
0.000000000 + x = 9.583148476 + 7.142857145
x = 9.583148476 + 7.142857145

Combine like terms: 9.583148476 + 7.142857145 = 16.726005621
x = 16.726005621

Simplifying
x = 16.726005621


Subproblem 2
x + -7.142857145 = -9.583148476

Simplifying
x + -7.142857145 = -9.583148476

Reorder the terms:
-7.142857145 + x = -9.583148476

Solving
-7.142857145 + x = -9.583148476

Solving for variable 'x'.

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

Add '7.142857145' to each side of the equation.
-7.142857145 + 7.142857145 + x = -9.583148476 + 7.142857145

Combine like terms: -7.142857145 + 7.142857145 = 0.000000000
0.000000000 + x = -9.583148476 + 7.142857145
x = -9.583148476 + 7.142857145

Combine like terms: -9.583148476 + 7.142857145 = -2.440291331
x = -2.440291331

Simplifying
x = -2.440291331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.726005621, -2.440291331}

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