4x^2+96x+1120=1280

Solution for 4x^2+96x+1120=1280 equation:

Simplifying
4x2 + 96x + 1120 = 1280

Reorder the terms:
1120 + 96x + 4x2 = 1280

Solving
1120 + 96x + 4x2 = 1280

Solving for variable 'x'.

Reorder the terms:
1120 + -1280 + 96x + 4x2 = 1280 + -1280

Combine like terms: 1120 + -1280 = -160
-160 + 96x + 4x2 = 1280 + -1280

Combine like terms: 1280 + -1280 = 0
-160 + 96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 24x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-40 + 24x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + 24x + x2 = 0

Solving
-40 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 24x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 24x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 24x + x2 = 0 + 40
24x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
24x + x2 = 40

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 40 + 144

Reorder the terms:
144 + 24x + x2 = 40 + 144

Combine like terms: 40 + 144 = 184
144 + 24x + x2 = 184

Factor a perfect square on the left side:
(x + 12)(x + 12) = 184

Calculate the square root of the right side: 13.564659966

Break this problem into two subproblems by setting 
(x + 12) equal to 13.564659966 and -13.564659966.

Subproblem 1
x + 12 = 13.564659966

Simplifying
x + 12 = 13.564659966

Reorder the terms:
12 + x = 13.564659966

Solving
12 + x = 13.564659966

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 13.564659966 + -12

Combine like terms: 12 + -12 = 0
0 + x = 13.564659966 + -12
x = 13.564659966 + -12

Combine like terms: 13.564659966 + -12 = 1.564659966
x = 1.564659966

Simplifying
x = 1.564659966

Subproblem 2
x + 12 = -13.564659966

Simplifying
x + 12 = -13.564659966

Reorder the terms:
12 + x = -13.564659966

Solving
12 + x = -13.564659966

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -13.564659966 + -12

Combine like terms: 12 + -12 = 0
0 + x = -13.564659966 + -12
x = -13.564659966 + -12

Combine like terms: -13.564659966 + -12 = -25.564659966
x = -25.564659966

Simplifying
x = -25.564659966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.564659966, -25.564659966}
Solution
x = {1.564659966, -25.564659966}