5x^2-70x+75=0

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Solution for 5x^2-70x+75=0 equation: 


Simplifying
5x2 + -70x + 75 = 0

Reorder the terms:
75 + -70x + 5x2 = 0

Solving
75 + -70x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + -14x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(15 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
15 + -14x + x2 = 0

Solving
15 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -14x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -14x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -14x + x2 = 0 + -15
-14x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-14x + x2 = -15

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -15 + 49

Reorder the terms:
49 + -14x + x2 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + -14x + x2 = 34

Factor a perfect square on the left side:
(x + -7)(x + -7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -7) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + -7 = 5.830951895

Simplifying
x + -7 = 5.830951895

Reorder the terms:
-7 + x = 5.830951895

Solving
-7 + x = 5.830951895

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.830951895 + 7
x = 5.830951895 + 7

Combine like terms: 5.830951895 + 7 = 12.830951895
x = 12.830951895

Simplifying
x = 12.830951895


Subproblem 2
x + -7 = -5.830951895

Simplifying
x + -7 = -5.830951895

Reorder the terms:
-7 + x = -5.830951895

Solving
-7 + x = -5.830951895

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.830951895 + 7
x = -5.830951895 + 7

Combine like terms: -5.830951895 + 7 = 1.169048105
x = 1.169048105

Simplifying
x = 1.169048105


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.830951895, 1.169048105}
Solution
x = {12.830951895, 1.169048105}

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