4x^2+84x-1120=0

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Solution for 4x^2+84x-1120=0 equation: 


Simplifying
4x2 + 84x + -1120 = 0

Reorder the terms:
-1120 + 84x + 4x2 = 0

Solving
-1120 + 84x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-280 + 21x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-280 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
-280 + 21x + x2 = 0

Solving
-280 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 21x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 21x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 21x + x2 = 0 + 280
21x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
21x + x2 = 280

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 280 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 280 + 110.25

Combine like terms: 280 + 110.25 = 390.25
110.25 + 21x + x2 = 390.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 390.25

Calculate the square root of the right side: 19.754746265

Break this problem into two subproblems by setting 
(x + 10.5) equal to 19.754746265 and -19.754746265.


Subproblem 1
x + 10.5 = 19.754746265

Simplifying
x + 10.5 = 19.754746265

Reorder the terms:
10.5 + x = 19.754746265

Solving
10.5 + x = 19.754746265

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 19.754746265 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 19.754746265 + -10.5
x = 19.754746265 + -10.5

Combine like terms: 19.754746265 + -10.5 = 9.254746265
x = 9.254746265

Simplifying
x = 9.254746265


Subproblem 2
x + 10.5 = -19.754746265

Simplifying
x + 10.5 = -19.754746265

Reorder the terms:
10.5 + x = -19.754746265

Solving
10.5 + x = -19.754746265

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -19.754746265 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -19.754746265 + -10.5
x = -19.754746265 + -10.5

Combine like terms: -19.754746265 + -10.5 = -30.254746265
x = -30.254746265

Simplifying
x = -30.254746265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.254746265, -30.254746265}
Solution
x = {9.254746265, -30.254746265}

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