10x+20x(x+5)=700

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Solution for 10x+20x(x+5)=700 equation: 


Simplifying
10x + 20x(x + 5) = 700

Reorder the terms:
10x + 20x(5 + x) = 700
10x + (5 * 20x + x * 20x) = 700
10x + (100x + 20x2) = 700

Combine like terms: 10x + 100x = 110x
110x + 20x2 = 700

Solving
110x + 20x2 = 700

Solving for variable 'x'.

Reorder the terms:
-700 + 110x + 20x2 = 700 + -700

Combine like terms: 700 + -700 = 0
-700 + 110x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-70 + 11x + 2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-70 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-70 + 11x + 2x2 = 0

Solving
-70 + 11x + 2x2 = 0

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

Divide each side by '2'.
-35 + 5.5x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 5.5x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 5.5x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 5.5x + x2 = 0 + 35
5.5x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
5.5x + x2 = 35

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 35 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 35 + 7.5625

Combine like terms: 35 + 7.5625 = 42.5625
7.5625 + 5.5x + x2 = 42.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 42.5625

Calculate the square root of the right side: 6.523994175

Break this problem into two subproblems by setting 
(x + 2.75) equal to 6.523994175 and -6.523994175.


Subproblem 1
x + 2.75 = 6.523994175

Simplifying
x + 2.75 = 6.523994175

Reorder the terms:
2.75 + x = 6.523994175

Solving
2.75 + x = 6.523994175

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 6.523994175 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 6.523994175 + -2.75
x = 6.523994175 + -2.75

Combine like terms: 6.523994175 + -2.75 = 3.773994175
x = 3.773994175

Simplifying
x = 3.773994175


Subproblem 2
x + 2.75 = -6.523994175

Simplifying
x + 2.75 = -6.523994175

Reorder the terms:
2.75 + x = -6.523994175

Solving
2.75 + x = -6.523994175

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -6.523994175 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -6.523994175 + -2.75
x = -6.523994175 + -2.75

Combine like terms: -6.523994175 + -2.75 = -9.273994175
x = -9.273994175

Simplifying
x = -9.273994175


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.773994175, -9.273994175}
Solution
x = {3.773994175, -9.273994175}

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