5x^2-175x+5=0

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Solution for 5x^2-175x+5=0 equation: 


Simplifying
5x2 + -175x + 5 = 0

Reorder the terms:
5 + -175x + 5x2 = 0

Solving
5 + -175x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -35x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -35x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -35x + x2 = 0

Solving
1 + -35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -35x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -35x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -35x + x2 = 0 + -1
-35x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-35x + x2 = -1

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -1 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -1 + 306.25

Combine like terms: -1 + 306.25 = 305.25
306.25 + -35x + x2 = 305.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 305.25

Calculate the square root of the right side: 17.47140521

Break this problem into two subproblems by setting 
(x + -17.5) equal to 17.47140521 and -17.47140521.


Subproblem 1
x + -17.5 = 17.47140521

Simplifying
x + -17.5 = 17.47140521

Reorder the terms:
-17.5 + x = 17.47140521

Solving
-17.5 + x = 17.47140521

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 17.47140521 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 17.47140521 + 17.5
x = 17.47140521 + 17.5

Combine like terms: 17.47140521 + 17.5 = 34.97140521
x = 34.97140521

Simplifying
x = 34.97140521


Subproblem 2
x + -17.5 = -17.47140521

Simplifying
x + -17.5 = -17.47140521

Reorder the terms:
-17.5 + x = -17.47140521

Solving
-17.5 + x = -17.47140521

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -17.47140521 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -17.47140521 + 17.5
x = -17.47140521 + 17.5

Combine like terms: -17.47140521 + 17.5 = 0.02859479
x = 0.02859479

Simplifying
x = 0.02859479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.97140521, 0.02859479}
Solution
x = {34.97140521, 0.02859479}

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