2x(x-10)=70

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Solution for 2x(x-10)=70 equation: 


Simplifying
2x(x + -10) = 70

Reorder the terms:
2x(-10 + x) = 70
(-10 * 2x + x * 2x) = 70
(-20x + 2x2) = 70

Solving
-20x + 2x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + -20x + 2x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + -10x + x2 = 0

Solving
-35 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -10x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -10x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -10x + x2 = 0 + 35
-10x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-10x + x2 = 35

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 35 + 25

Reorder the terms:
25 + -10x + x2 = 35 + 25

Combine like terms: 35 + 25 = 60
25 + -10x + x2 = 60

Factor a perfect square on the left side:
(x + -5)(x + -5) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + -5) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + -5 = 7.745966692

Simplifying
x + -5 = 7.745966692

Reorder the terms:
-5 + x = 7.745966692

Solving
-5 + x = 7.745966692

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 7.745966692 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.745966692 + 5
x = 7.745966692 + 5

Combine like terms: 7.745966692 + 5 = 12.745966692
x = 12.745966692

Simplifying
x = 12.745966692


Subproblem 2
x + -5 = -7.745966692

Simplifying
x + -5 = -7.745966692

Reorder the terms:
-5 + x = -7.745966692

Solving
-5 + x = -7.745966692

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -7.745966692 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.745966692 + 5
x = -7.745966692 + 5

Combine like terms: -7.745966692 + 5 = -2.745966692
x = -2.745966692

Simplifying
x = -2.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.745966692, -2.745966692}
Solution
x = {12.745966692, -2.745966692}

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