5x(2x-8)=35

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Solution for 5x(2x-8)=35 equation: 


Simplifying
5x(2x + -8) = 35

Reorder the terms:
5x(-8 + 2x) = 35
(-8 * 5x + 2x * 5x) = 35
(-40x + 10x2) = 35

Solving
-40x + 10x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -40x + 10x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -40x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -8x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -8x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + -8x + 2x2 = 0

Solving
-7 + -8x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3.5 + -4x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -4x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -4x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -4x + x2 = 0 + 3.5
-4x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-4x + x2 = 3.5

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 = 3.5 + 4

Reorder the terms:
4 + -4x + x2 = 3.5 + 4

Combine like terms: 3.5 + 4 = 7.5
4 + -4x + x2 = 7.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(x + -2) equal to 2.738612788 and -2.738612788.


Subproblem 1
x + -2 = 2.738612788

Simplifying
x + -2 = 2.738612788

Reorder the terms:
-2 + x = 2.738612788

Solving
-2 + x = 2.738612788

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 = 2.738612788 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.738612788 + 2
x = 2.738612788 + 2

Combine like terms: 2.738612788 + 2 = 4.738612788
x = 4.738612788

Simplifying
x = 4.738612788


Subproblem 2
x + -2 = -2.738612788

Simplifying
x + -2 = -2.738612788

Reorder the terms:
-2 + x = -2.738612788

Solving
-2 + x = -2.738612788

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 = -2.738612788 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.738612788 + 2
x = -2.738612788 + 2

Combine like terms: -2.738612788 + 2 = -0.738612788
x = -0.738612788

Simplifying
x = -0.738612788


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.738612788, -0.738612788}
Solution
x = {4.738612788, -0.738612788}

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