5x(x-4)=70

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Solution for 5x(x-4)=70 equation: 


Simplifying
5x(x + -4) = 70

Reorder the terms:
5x(-4 + x) = 70
(-4 * 5x + x * 5x) = 70
(-20x + 5x2) = 70

Solving
-20x + 5x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + -20x + 5x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-14 + -4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-14 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + -4x + x2 = 0

Solving
-14 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -4x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -4x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -4x + x2 = 0 + 14
-4x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-4x + x2 = 14

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 = 14 + 4

Reorder the terms:
4 + -4x + x2 = 14 + 4

Combine like terms: 14 + 4 = 18
4 + -4x + x2 = 18

Factor a perfect square on the left side:
(x + -2)(x + -2) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -2) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -2 = 4.242640687

Simplifying
x + -2 = 4.242640687

Reorder the terms:
-2 + x = 4.242640687

Solving
-2 + x = 4.242640687

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 = 4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.242640687 + 2
x = 4.242640687 + 2

Combine like terms: 4.242640687 + 2 = 6.242640687
x = 6.242640687

Simplifying
x = 6.242640687


Subproblem 2
x + -2 = -4.242640687

Simplifying
x + -2 = -4.242640687

Reorder the terms:
-2 + x = -4.242640687

Solving
-2 + x = -4.242640687

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 = -4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.242640687 + 2
x = -4.242640687 + 2

Combine like terms: -4.242640687 + 2 = -2.242640687
x = -2.242640687

Simplifying
x = -2.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.242640687, -2.242640687}
Solution
x = {6.242640687, -2.242640687}

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