196x^2-4=400x+596

Solution for 196x^2-4=400x+596 equation:

Simplifying
196x2 + -4 = 400x + 596

Reorder the terms:
-4 + 196x2 = 400x + 596

Reorder the terms:
-4 + 196x2 = 596 + 400x

Solving
-4 + 196x2 = 596 + 400x

Solving for variable 'x'.

Reorder the terms:
-4 + -596 + -400x + 196x2 = 596 + 400x + -596 + -400x

Combine like terms: -4 + -596 = -600
-600 + -400x + 196x2 = 596 + 400x + -596 + -400x

Reorder the terms:
-600 + -400x + 196x2 = 596 + -596 + 400x + -400x

Combine like terms: 596 + -596 = 0
-600 + -400x + 196x2 = 0 + 400x + -400x
-600 + -400x + 196x2 = 400x + -400x

Combine like terms: 400x + -400x = 0
-600 + -400x + 196x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-150 + -100x + 49x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-150 + -100x + 49x2)' equal to zero and attempt to solve:

Simplifying
-150 + -100x + 49x2 = 0

Solving
-150 + -100x + 49x2 = 0

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

Divide each side by '49'.
-3.06122449 + -2.040816327x + x2 = 0

Move the constant term to the right:

Add '3.06122449' to each side of the equation.
-3.06122449 + -2.040816327x + 3.06122449 + x2 = 0 + 3.06122449

Reorder the terms:
-3.06122449 + 3.06122449 + -2.040816327x + x2 = 0 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + -2.040816327x + x2 = 0 + 3.06122449
-2.040816327x + x2 = 0 + 3.06122449

Combine like terms: 0 + 3.06122449 = 3.06122449
-2.040816327x + x2 = 3.06122449

The x term is -2.040816327x.  Take half its coefficient (-1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
-2.040816327x + 1.041232821 + x2 = 3.06122449 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327x + x2 = 3.06122449 + 1.041232821

Combine like terms: 3.06122449 + 1.041232821 = 4.102457311
1.041232821 + -2.040816327x + x2 = 4.102457311

Factor a perfect square on the left side:
(x + -1.020408164)(x + -1.020408164) = 4.102457311

Calculate the square root of the right side: 2.025452372

Break this problem into two subproblems by setting 
(x + -1.020408164) equal to 2.025452372 and -2.025452372.

Subproblem 1
x + -1.020408164 = 2.025452372

Simplifying
x + -1.020408164 = 2.025452372

Reorder the terms:
-1.020408164 + x = 2.025452372

Solving
-1.020408164 + x = 2.025452372

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = 2.025452372 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = 2.025452372 + 1.020408164
x = 2.025452372 + 1.020408164

Combine like terms: 2.025452372 + 1.020408164 = 3.045860536
x = 3.045860536

Simplifying
x = 3.045860536

Subproblem 2
x + -1.020408164 = -2.025452372

Simplifying
x + -1.020408164 = -2.025452372

Reorder the terms:
-1.020408164 + x = -2.025452372

Solving
-1.020408164 + x = -2.025452372

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = -2.025452372 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = -2.025452372 + 1.020408164
x = -2.025452372 + 1.020408164

Combine like terms: -2.025452372 + 1.020408164 = -1.005044208
x = -1.005044208

Simplifying
x = -1.005044208

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.045860536, -1.005044208}
Solution
x = {3.045860536, -1.005044208}