(x+10)(x)(20)=700

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Solution for (x+10)(x)(20)=700 equation: 


Simplifying
(x + 10)(x)(20) = 700

Reorder the terms:
(10 + x)(x)(20) = 700

Reorder the terms for easier multiplication:
20x(10 + x) = 700
(10 * 20x + x * 20x) = 700
(200x + 20x2) = 700

Solving
200x + 20x2 = 700

Solving for variable 'x'.

Reorder the terms:
-700 + 200x + 20x2 = 700 + -700

Combine like terms: 700 + -700 = 0
-700 + 200x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-35 + 10x + x2) = 0

Ignore the factor 20.

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 = 2.745966692
x = 2.745966692

Simplifying
x = 2.745966692


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 = -12.745966692
x = -12.745966692

Simplifying
x = -12.745966692


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

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