4x^2-40x+25=0

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Solution for 4x^2-40x+25=0 equation: 


Simplifying
4x2 + -40x + 25 = 0

Reorder the terms:
25 + -40x + 4x2 = 0

Solving
25 + -40x + 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 + -10x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -10x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -10x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -10x + x2 = 0 + -6.25
-10x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-10x + x2 = -6.25

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 = -6.25 + 25

Reorder the terms:
25 + -10x + x2 = -6.25 + 25

Combine like terms: -6.25 + 25 = 18.75
25 + -10x + x2 = 18.75

Factor a perfect square on the left side:
(x + -5)(x + -5) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(x + -5) equal to 4.330127019 and -4.330127019.


Subproblem 1
x + -5 = 4.330127019

Simplifying
x + -5 = 4.330127019

Reorder the terms:
-5 + x = 4.330127019

Solving
-5 + x = 4.330127019

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 = 4.330127019 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.330127019 + 5
x = 4.330127019 + 5

Combine like terms: 4.330127019 + 5 = 9.330127019
x = 9.330127019

Simplifying
x = 9.330127019


Subproblem 2
x + -5 = -4.330127019

Simplifying
x + -5 = -4.330127019

Reorder the terms:
-5 + x = -4.330127019

Solving
-5 + x = -4.330127019

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 = -4.330127019 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.330127019 + 5
x = -4.330127019 + 5

Combine like terms: -4.330127019 + 5 = 0.669872981
x = 0.669872981

Simplifying
x = 0.669872981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.330127019, 0.669872981}

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