4x^2-25x+2=0

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


Simplifying
4x2 + -25x + 2 = 0

Reorder the terms:
2 + -25x + 4x2 = 0

Solving
2 + -25x + 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'.
0.5 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -6.25x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -6.25x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -6.25x + x2 = 0 + -0.5
-6.25x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-6.25x + x2 = -0.5

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -0.5 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -0.5 + 9.765625

Combine like terms: -0.5 + 9.765625 = 9.265625
9.765625 + -6.25x + x2 = 9.265625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 9.265625

Calculate the square root of the right side: 3.043948915

Break this problem into two subproblems by setting 
(x + -3.125) equal to 3.043948915 and -3.043948915.


Subproblem 1
x + -3.125 = 3.043948915

Simplifying
x + -3.125 = 3.043948915

Reorder the terms:
-3.125 + x = 3.043948915

Solving
-3.125 + x = 3.043948915

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 3.043948915 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 3.043948915 + 3.125
x = 3.043948915 + 3.125

Combine like terms: 3.043948915 + 3.125 = 6.168948915
x = 6.168948915

Simplifying
x = 6.168948915


Subproblem 2
x + -3.125 = -3.043948915

Simplifying
x + -3.125 = -3.043948915

Reorder the terms:
-3.125 + x = -3.043948915

Solving
-3.125 + x = -3.043948915

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -3.043948915 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -3.043948915 + 3.125
x = -3.043948915 + 3.125

Combine like terms: -3.043948915 + 3.125 = 0.081051085
x = 0.081051085

Simplifying
x = 0.081051085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.168948915, 0.081051085}

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