5x(2x-10)=35

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Solution for 5x(2x-10)=35 equation: 


Simplifying
5x(2x + -10) = 35

Reorder the terms:
5x(-10 + 2x) = 35
(-10 * 5x + 2x * 5x) = 35
(-50x + 10x2) = 35

Solving
-50x + 10x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -50x + 10x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -50x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -10x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + -10x + 2x2 = 0

Solving
-7 + -10x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -5x + x2 = 0 + 3.5
-5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-5x + x2 = 3.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 3.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3.5 + 6.25

Combine like terms: 3.5 + 6.25 = 9.75
6.25 + -5x + x2 = 9.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + -2.5 = 3.122498999

Simplifying
x + -2.5 = 3.122498999

Reorder the terms:
-2.5 + x = 3.122498999

Solving
-2.5 + x = 3.122498999

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.122498999 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.122498999 + 2.5
x = 3.122498999 + 2.5

Combine like terms: 3.122498999 + 2.5 = 5.622498999
x = 5.622498999

Simplifying
x = 5.622498999


Subproblem 2
x + -2.5 = -3.122498999

Simplifying
x + -2.5 = -3.122498999

Reorder the terms:
-2.5 + x = -3.122498999

Solving
-2.5 + x = -3.122498999

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.122498999 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.122498999 + 2.5
x = -3.122498999 + 2.5

Combine like terms: -3.122498999 + 2.5 = -0.622498999
x = -0.622498999

Simplifying
x = -0.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.622498999, -0.622498999}
Solution
x = {5.622498999, -0.622498999}

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