2(x^2-39x+70)=0

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Solution for 2(x^2-39x+70)=0 equation: 


Simplifying
2(x2 + -39x + 70) = 0

Reorder the terms:
2(70 + -39x + x2) = 0
(70 * 2 + -39x * 2 + x2 * 2) = 0
(140 + -78x + 2x2) = 0

Solving
140 + -78x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(70 + -39x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(70 + -39x + x2)' equal to zero and attempt to solve:

Simplifying
70 + -39x + x2 = 0

Solving
70 + -39x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-70' to each side of the equation.
70 + -39x + -70 + x2 = 0 + -70

Reorder the terms:
70 + -70 + -39x + x2 = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -39x + x2 = 0 + -70
-39x + x2 = 0 + -70

Combine like terms: 0 + -70 = -70
-39x + x2 = -70

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = -70 + 380.25

Reorder the terms:
380.25 + -39x + x2 = -70 + 380.25

Combine like terms: -70 + 380.25 = 310.25
380.25 + -39x + x2 = 310.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 310.25

Calculate the square root of the right side: 17.613914954

Break this problem into two subproblems by setting 
(x + -19.5) equal to 17.613914954 and -17.613914954.


Subproblem 1
x + -19.5 = 17.613914954

Simplifying
x + -19.5 = 17.613914954

Reorder the terms:
-19.5 + x = 17.613914954

Solving
-19.5 + x = 17.613914954

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = 17.613914954 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = 17.613914954 + 19.5
x = 17.613914954 + 19.5

Combine like terms: 17.613914954 + 19.5 = 37.113914954
x = 37.113914954

Simplifying
x = 37.113914954


Subproblem 2
x + -19.5 = -17.613914954

Simplifying
x + -19.5 = -17.613914954

Reorder the terms:
-19.5 + x = -17.613914954

Solving
-19.5 + x = -17.613914954

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = -17.613914954 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = -17.613914954 + 19.5
x = -17.613914954 + 19.5

Combine like terms: -17.613914954 + 19.5 = 1.886085046
x = 1.886085046

Simplifying
x = 1.886085046


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.113914954, 1.886085046}
Solution
x = {37.113914954, 1.886085046}

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