5=16X^2+160X+1

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Solution for 5=16X^2+160X+1 equation: 


Simplifying
5 = 16X2 + 160X + 1

Reorder the terms:
5 = 1 + 160X + 16X2

Solving
5 = 1 + 160X + 16X2

Solving for variable 'X'.

Combine like terms: 5 + -1 = 4
4 + -160X + -16X2 = 1 + 160X + 16X2 + -1 + -160X + -16X2

Reorder the terms:
4 + -160X + -16X2 = 1 + -1 + 160X + -160X + 16X2 + -16X2

Combine like terms: 1 + -1 = 0
4 + -160X + -16X2 = 0 + 160X + -160X + 16X2 + -16X2
4 + -160X + -16X2 = 160X + -160X + 16X2 + -16X2

Combine like terms: 160X + -160X = 0
4 + -160X + -16X2 = 0 + 16X2 + -16X2
4 + -160X + -16X2 = 16X2 + -16X2

Combine like terms: 16X2 + -16X2 = 0
4 + -160X + -16X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -40X + -4X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -40X + -4X2)' equal to zero and attempt to solve:

Simplifying
1 + -40X + -4X2 = 0

Solving
1 + -40X + -4X2 = 0

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

Divide each side by '-4'.
-0.25 + 10X + X2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 10X + 0.25 + X2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 10X + X2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 10X + X2 = 0 + 0.25
10X + X2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
10X + X2 = 0.25

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 = 0.25 + 25

Reorder the terms:
25 + 10X + X2 = 0.25 + 25

Combine like terms: 0.25 + 25 = 25.25
25 + 10X + X2 = 25.25

Factor a perfect square on the left side:
(X + 5)(X + 5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(X + 5) equal to 5.024937811 and -5.024937811.


Subproblem 1
X + 5 = 5.024937811

Simplifying
X + 5 = 5.024937811

Reorder the terms:
5 + X = 5.024937811

Solving
5 + X = 5.024937811

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 = 5.024937811 + -5

Combine like terms: 5 + -5 = 0
0 + X = 5.024937811 + -5
X = 5.024937811 + -5

Combine like terms: 5.024937811 + -5 = 0.024937811
X = 0.024937811

Simplifying
X = 0.024937811


Subproblem 2
X + 5 = -5.024937811

Simplifying
X + 5 = -5.024937811

Reorder the terms:
5 + X = -5.024937811

Solving
5 + X = -5.024937811

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 = -5.024937811 + -5

Combine like terms: 5 + -5 = 0
0 + X = -5.024937811 + -5
X = -5.024937811 + -5

Combine like terms: -5.024937811 + -5 = -10.024937811
X = -10.024937811

Simplifying
X = -10.024937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.024937811, -10.024937811}
Solution
X = {0.024937811, -10.024937811}

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