437x^2+103x+11=79x^2+43x+2089

Solution for 437x^2+103x+11=79x^2+43x+2089 equation:

Simplifying
437x2 + 103x + 11 = 79x2 + 43x + 2089

Reorder the terms:
11 + 103x + 437x2 = 79x2 + 43x + 2089

Reorder the terms:
11 + 103x + 437x2 = 2089 + 43x + 79x2

Solving
11 + 103x + 437x2 = 2089 + 43x + 79x2

Solving for variable 'x'.

Reorder the terms:
11 + -2089 + 103x + -43x + 437x2 + -79x2 = 2089 + 43x + 79x2 + -2089 + -43x + -79x2

Combine like terms: 11 + -2089 = -2078
-2078 + 103x + -43x + 437x2 + -79x2 = 2089 + 43x + 79x2 + -2089 + -43x + -79x2

Combine like terms: 103x + -43x = 60x
-2078 + 60x + 437x2 + -79x2 = 2089 + 43x + 79x2 + -2089 + -43x + -79x2

Combine like terms: 437x2 + -79x2 = 358x2
-2078 + 60x + 358x2 = 2089 + 43x + 79x2 + -2089 + -43x + -79x2

Reorder the terms:
-2078 + 60x + 358x2 = 2089 + -2089 + 43x + -43x + 79x2 + -79x2

Combine like terms: 2089 + -2089 = 0
-2078 + 60x + 358x2 = 0 + 43x + -43x + 79x2 + -79x2
-2078 + 60x + 358x2 = 43x + -43x + 79x2 + -79x2

Combine like terms: 43x + -43x = 0
-2078 + 60x + 358x2 = 0 + 79x2 + -79x2
-2078 + 60x + 358x2 = 79x2 + -79x2

Combine like terms: 79x2 + -79x2 = 0
-2078 + 60x + 358x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1039 + 30x + 179x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1039 + 30x + 179x2)' equal to zero and attempt to solve:

Simplifying
-1039 + 30x + 179x2 = 0

Solving
-1039 + 30x + 179x2 = 0

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

Divide each side by '179'.
-5.804469274 + 0.1675977654x + x2 = 0

Move the constant term to the right:

Add '5.804469274' to each side of the equation.
-5.804469274 + 0.1675977654x + 5.804469274 + x2 = 0 + 5.804469274

Reorder the terms:
-5.804469274 + 5.804469274 + 0.1675977654x + x2 = 0 + 5.804469274

Combine like terms: -5.804469274 + 5.804469274 = 0.000000000
0.000000000 + 0.1675977654x + x2 = 0 + 5.804469274
0.1675977654x + x2 = 0 + 5.804469274

Combine like terms: 0 + 5.804469274 = 5.804469274
0.1675977654x + x2 = 5.804469274

The x term is 0.1675977654x.  Take half its coefficient (0.0837988827).
Square it (0.007022252742) and add it to both sides.

Add '0.007022252742' to each side of the equation.
0.1675977654x + 0.007022252742 + x2 = 5.804469274 + 0.007022252742

Reorder the terms:
0.007022252742 + 0.1675977654x + x2 = 5.804469274 + 0.007022252742

Combine like terms: 5.804469274 + 0.007022252742 = 5.811491526742
0.007022252742 + 0.1675977654x + x2 = 5.811491526742

Factor a perfect square on the left side:
(x + 0.0837988827)(x + 0.0837988827) = 5.811491526742

Calculate the square root of the right side: 2.410703534

Break this problem into two subproblems by setting 
(x + 0.0837988827) equal to 2.410703534 and -2.410703534.

Subproblem 1
x + 0.0837988827 = 2.410703534

Simplifying
x + 0.0837988827 = 2.410703534

Reorder the terms:
0.0837988827 + x = 2.410703534

Solving
0.0837988827 + x = 2.410703534

Solving for variable 'x'.

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

Add '-0.0837988827' to each side of the equation.
0.0837988827 + -0.0837988827 + x = 2.410703534 + -0.0837988827

Combine like terms: 0.0837988827 + -0.0837988827 = 0.0000000000
0.0000000000 + x = 2.410703534 + -0.0837988827
x = 2.410703534 + -0.0837988827

Combine like terms: 2.410703534 + -0.0837988827 = 2.3269046513
x = 2.3269046513

Simplifying
x = 2.3269046513

Subproblem 2
x + 0.0837988827 = -2.410703534

Simplifying
x + 0.0837988827 = -2.410703534

Reorder the terms:
0.0837988827 + x = -2.410703534

Solving
0.0837988827 + x = -2.410703534

Solving for variable 'x'.

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

Add '-0.0837988827' to each side of the equation.
0.0837988827 + -0.0837988827 + x = -2.410703534 + -0.0837988827

Combine like terms: 0.0837988827 + -0.0837988827 = 0.0000000000
0.0000000000 + x = -2.410703534 + -0.0837988827
x = -2.410703534 + -0.0837988827

Combine like terms: -2.410703534 + -0.0837988827 = -2.4945024167
x = -2.4945024167

Simplifying
x = -2.4945024167

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3269046513, -2.4945024167}
Solution
x = {2.3269046513, -2.4945024167}