4x^2-20x-112=0

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Solution for 4x^2-20x-112=0 equation: 


Simplifying
4x2 + -20x + -112 = 0

Reorder the terms:
-112 + -20x + 4x2 = 0

Solving
-112 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + -5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -5x + x2 = 0

Solving
-28 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -5x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -5x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -5x + x2 = 0 + 28
-5x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-5x + x2 = 28

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 28 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + -5x + x2 = 34.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + -2.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
x + -2.5 = 5.852349955

Simplifying
x + -2.5 = 5.852349955

Reorder the terms:
-2.5 + x = 5.852349955

Solving
-2.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 5.852349955 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 5.852349955 + 2.5
x = 5.852349955 + 2.5

Combine like terms: 5.852349955 + 2.5 = 8.352349955
x = 8.352349955

Simplifying
x = 8.352349955


Subproblem 2
x + -2.5 = -5.852349955

Simplifying
x + -2.5 = -5.852349955

Reorder the terms:
-2.5 + x = -5.852349955

Solving
-2.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -5.852349955 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -5.852349955 + 2.5
x = -5.852349955 + 2.5

Combine like terms: -5.852349955 + 2.5 = -3.352349955
x = -3.352349955

Simplifying
x = -3.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.352349955, -3.352349955}
Solution
x = {8.352349955, -3.352349955}

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