16x^2-120x+25=0

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Solution for 16x^2-120x+25=0 equation: 


Simplifying
16x2 + -120x + 25 = 0

Reorder the terms:
25 + -120x + 16x2 = 0

Solving
25 + -120x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
1.5625 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-1.5625' to each side of the equation.
1.5625 + -7.5x + -1.5625 + x2 = 0 + -1.5625

Reorder the terms:
1.5625 + -1.5625 + -7.5x + x2 = 0 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + -7.5x + x2 = 0 + -1.5625
-7.5x + x2 = 0 + -1.5625

Combine like terms: 0 + -1.5625 = -1.5625
-7.5x + x2 = -1.5625

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -1.5625 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -1.5625 + 14.0625

Combine like terms: -1.5625 + 14.0625 = 12.5
14.0625 + -7.5x + x2 = 12.5

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.535533906 and -3.535533906.


Subproblem 1
x + -3.75 = 3.535533906

Simplifying
x + -3.75 = 3.535533906

Reorder the terms:
-3.75 + x = 3.535533906

Solving
-3.75 + x = 3.535533906

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.535533906 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.535533906 + 3.75
x = 3.535533906 + 3.75

Combine like terms: 3.535533906 + 3.75 = 7.285533906
x = 7.285533906

Simplifying
x = 7.285533906


Subproblem 2
x + -3.75 = -3.535533906

Simplifying
x + -3.75 = -3.535533906

Reorder the terms:
-3.75 + x = -3.535533906

Solving
-3.75 + x = -3.535533906

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.535533906 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.535533906 + 3.75
x = -3.535533906 + 3.75

Combine like terms: -3.535533906 + 3.75 = 0.214466094
x = 0.214466094

Simplifying
x = 0.214466094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.285533906, 0.214466094}

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