5x^2-105x+175=0

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Solution for 5x^2-105x+175=0 equation: 


Simplifying
5x2 + -105x + 175 = 0

Reorder the terms:
175 + -105x + 5x2 = 0

Solving
175 + -105x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(35 + -21x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(35 + -21x + x2)' equal to zero and attempt to solve:

Simplifying
35 + -21x + x2 = 0

Solving
35 + -21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -21x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -21x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -21x + x2 = 0 + -35
-21x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-21x + x2 = -35

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -35 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -35 + 110.25

Combine like terms: -35 + 110.25 = 75.25
110.25 + -21x + x2 = 75.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 75.25

Calculate the square root of the right side: 8.674675786

Break this problem into two subproblems by setting 
(x + -10.5) equal to 8.674675786 and -8.674675786.


Subproblem 1
x + -10.5 = 8.674675786

Simplifying
x + -10.5 = 8.674675786

Reorder the terms:
-10.5 + x = 8.674675786

Solving
-10.5 + x = 8.674675786

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 8.674675786 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 8.674675786 + 10.5
x = 8.674675786 + 10.5

Combine like terms: 8.674675786 + 10.5 = 19.174675786
x = 19.174675786

Simplifying
x = 19.174675786


Subproblem 2
x + -10.5 = -8.674675786

Simplifying
x + -10.5 = -8.674675786

Reorder the terms:
-10.5 + x = -8.674675786

Solving
-10.5 + x = -8.674675786

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -8.674675786 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -8.674675786 + 10.5
x = -8.674675786 + 10.5

Combine like terms: -8.674675786 + 10.5 = 1.825324214
x = 1.825324214

Simplifying
x = 1.825324214


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.174675786, 1.825324214}
Solution
x = {19.174675786, 1.825324214}

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