4x^2+17x-196=0

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Solution for 4x^2+17x-196=0 equation: 


Simplifying
4x2 + 17x + -196 = 0

Reorder the terms:
-196 + 17x + 4x2 = 0

Solving
-196 + 17x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-49 + 4.25x + x2 = 0

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 4.25x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + 4.25x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 4.25x + x2 = 0 + 49
4.25x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
4.25x + x2 = 49

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 49 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 49 + 4.515625

Combine like terms: 49 + 4.515625 = 53.515625
4.515625 + 4.25x + x2 = 53.515625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 53.515625

Calculate the square root of the right side: 7.315437444

Break this problem into two subproblems by setting 
(x + 2.125) equal to 7.315437444 and -7.315437444.


Subproblem 1
x + 2.125 = 7.315437444

Simplifying
x + 2.125 = 7.315437444

Reorder the terms:
2.125 + x = 7.315437444

Solving
2.125 + x = 7.315437444

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 7.315437444 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 7.315437444 + -2.125
x = 7.315437444 + -2.125

Combine like terms: 7.315437444 + -2.125 = 5.190437444
x = 5.190437444

Simplifying
x = 5.190437444


Subproblem 2
x + 2.125 = -7.315437444

Simplifying
x + 2.125 = -7.315437444

Reorder the terms:
2.125 + x = -7.315437444

Solving
2.125 + x = -7.315437444

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -7.315437444 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -7.315437444 + -2.125
x = -7.315437444 + -2.125

Combine like terms: -7.315437444 + -2.125 = -9.440437444
x = -9.440437444

Simplifying
x = -9.440437444


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.190437444, -9.440437444}

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