4x^2-38x+25=0

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Solution for 4x^2-38x+25=0 equation: 


Simplifying
4x2 + -38x + 25 = 0

Reorder the terms:
25 + -38x + 4x2 = 0

Solving
25 + -38x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
6.25 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -9.5x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -9.5x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -9.5x + x2 = 0 + -6.25
-9.5x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-9.5x + x2 = -6.25

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -6.25 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -6.25 + 22.5625

Combine like terms: -6.25 + 22.5625 = 16.3125
22.5625 + -9.5x + x2 = 16.3125

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 16.3125

Calculate the square root of the right side: 4.038873605

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.038873605 and -4.038873605.


Subproblem 1
x + -4.75 = 4.038873605

Simplifying
x + -4.75 = 4.038873605

Reorder the terms:
-4.75 + x = 4.038873605

Solving
-4.75 + x = 4.038873605

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 4.038873605 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 4.038873605 + 4.75
x = 4.038873605 + 4.75

Combine like terms: 4.038873605 + 4.75 = 8.788873605
x = 8.788873605

Simplifying
x = 8.788873605


Subproblem 2
x + -4.75 = -4.038873605

Simplifying
x + -4.75 = -4.038873605

Reorder the terms:
-4.75 + x = -4.038873605

Solving
-4.75 + x = -4.038873605

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -4.038873605 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -4.038873605 + 4.75
x = -4.038873605 + 4.75

Combine like terms: -4.038873605 + 4.75 = 0.711126395
x = 0.711126395

Simplifying
x = 0.711126395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.788873605, 0.711126395}

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