16x^2+160x-300=0

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Solution for 16x^2+160x-300=0 equation: 


Simplifying
16x2 + 160x + -300 = 0

Reorder the terms:
-300 + 160x + 16x2 = 0

Solving
-300 + 160x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-75 + 40x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-75 + 40x + 4x2)' equal to zero and attempt to solve:

Simplifying
-75 + 40x + 4x2 = 0

Solving
-75 + 40x + 4x2 = 0

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

Divide each side by '4'.
-18.75 + 10x + x2 = 0

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 10x + 18.75 + x2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + 10x + x2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 10x + x2 = 0 + 18.75
10x + x2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
10x + x2 = 18.75

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 18.75 + 25

Reorder the terms:
25 + 10x + x2 = 18.75 + 25

Combine like terms: 18.75 + 25 = 43.75
25 + 10x + x2 = 43.75

Factor a perfect square on the left side:
(x + 5)(x + 5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(x + 5) equal to 6.614378278 and -6.614378278.


Subproblem 1
x + 5 = 6.614378278

Simplifying
x + 5 = 6.614378278

Reorder the terms:
5 + x = 6.614378278

Solving
5 + x = 6.614378278

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 6.614378278 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.614378278 + -5
x = 6.614378278 + -5

Combine like terms: 6.614378278 + -5 = 1.614378278
x = 1.614378278

Simplifying
x = 1.614378278


Subproblem 2
x + 5 = -6.614378278

Simplifying
x + 5 = -6.614378278

Reorder the terms:
5 + x = -6.614378278

Solving
5 + x = -6.614378278

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -6.614378278 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.614378278 + -5
x = -6.614378278 + -5

Combine like terms: -6.614378278 + -5 = -11.614378278
x = -11.614378278

Simplifying
x = -11.614378278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.614378278, -11.614378278}
Solution
x = {1.614378278, -11.614378278}

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