2x(x-4)=70

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Solution for 2x(x-4)=70 equation: 


Simplifying
2x(x + -4) = 70

Reorder the terms:
2x(-4 + x) = 70
(-4 * 2x + x * 2x) = 70
(-8x + 2x2) = 70

Solving
-8x + 2x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + -8x + 2x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + -4x + x2 = 0

Solving
-35 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -4x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -4x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -4x + x2 = 0 + 35
-4x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-4x + x2 = 35

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 35 + 4

Reorder the terms:
4 + -4x + x2 = 35 + 4

Combine like terms: 35 + 4 = 39
4 + -4x + x2 = 39

Factor a perfect square on the left side:
(x + -2)(x + -2) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -2) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + -2 = 6.244997998

Simplifying
x + -2 = 6.244997998

Reorder the terms:
-2 + x = 6.244997998

Solving
-2 + x = 6.244997998

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.244997998 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.244997998 + 2
x = 6.244997998 + 2

Combine like terms: 6.244997998 + 2 = 8.244997998
x = 8.244997998

Simplifying
x = 8.244997998


Subproblem 2
x + -2 = -6.244997998

Simplifying
x + -2 = -6.244997998

Reorder the terms:
-2 + x = -6.244997998

Solving
-2 + x = -6.244997998

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.244997998 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.244997998 + 2
x = -6.244997998 + 2

Combine like terms: -6.244997998 + 2 = -4.244997998
x = -4.244997998

Simplifying
x = -4.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.244997998, -4.244997998}
Solution
x = {8.244997998, -4.244997998}

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