2x^2+70x-196=0

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Solution for 2x^2+70x-196=0 equation: 


Simplifying
2x2 + 70x + -196 = 0

Reorder the terms:
-196 + 70x + 2x2 = 0

Solving
-196 + 70x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-98 + 35x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-98 + 35x + x2)' equal to zero and attempt to solve:

Simplifying
-98 + 35x + x2 = 0

Solving
-98 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + 35x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + 35x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 35x + x2 = 0 + 98
35x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
35x + x2 = 98

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 98 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 98 + 306.25

Combine like terms: 98 + 306.25 = 404.25
306.25 + 35x + x2 = 404.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 404.25

Calculate the square root of the right side: 20.105969263

Break this problem into two subproblems by setting 
(x + 17.5) equal to 20.105969263 and -20.105969263.


Subproblem 1
x + 17.5 = 20.105969263

Simplifying
x + 17.5 = 20.105969263

Reorder the terms:
17.5 + x = 20.105969263

Solving
17.5 + x = 20.105969263

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 20.105969263 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 20.105969263 + -17.5
x = 20.105969263 + -17.5

Combine like terms: 20.105969263 + -17.5 = 2.605969263
x = 2.605969263

Simplifying
x = 2.605969263


Subproblem 2
x + 17.5 = -20.105969263

Simplifying
x + 17.5 = -20.105969263

Reorder the terms:
17.5 + x = -20.105969263

Solving
17.5 + x = -20.105969263

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -20.105969263 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -20.105969263 + -17.5
x = -20.105969263 + -17.5

Combine like terms: -20.105969263 + -17.5 = -37.605969263
x = -37.605969263

Simplifying
x = -37.605969263


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.605969263, -37.605969263}
Solution
x = {2.605969263, -37.605969263}

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