20x+5x(x+7)=310

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Solution for 20x+5x(x+7)=310 equation: 


Simplifying
20x + 5x(x + 7) = 310

Reorder the terms:
20x + 5x(7 + x) = 310
20x + (7 * 5x + x * 5x) = 310
20x + (35x + 5x2) = 310

Combine like terms: 20x + 35x = 55x
55x + 5x2 = 310

Solving
55x + 5x2 = 310

Solving for variable 'x'.

Reorder the terms:
-310 + 55x + 5x2 = 310 + -310

Combine like terms: 310 + -310 = 0
-310 + 55x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-62 + 11x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-62 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-62 + 11x + x2 = 0

Solving
-62 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + 11x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + 11x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + 11x + x2 = 0 + 62
11x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
11x + x2 = 62

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 62 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 62 + 30.25

Combine like terms: 62 + 30.25 = 92.25
30.25 + 11x + x2 = 92.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + 5.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + 5.5 = 9.604686356

Simplifying
x + 5.5 = 9.604686356

Reorder the terms:
5.5 + x = 9.604686356

Solving
5.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 9.604686356 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 9.604686356 + -5.5
x = 9.604686356 + -5.5

Combine like terms: 9.604686356 + -5.5 = 4.104686356
x = 4.104686356

Simplifying
x = 4.104686356


Subproblem 2
x + 5.5 = -9.604686356

Simplifying
x + 5.5 = -9.604686356

Reorder the terms:
5.5 + x = -9.604686356

Solving
5.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -9.604686356 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -9.604686356 + -5.5
x = -9.604686356 + -5.5

Combine like terms: -9.604686356 + -5.5 = -15.104686356
x = -15.104686356

Simplifying
x = -15.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.104686356, -15.104686356}
Solution
x = {4.104686356, -15.104686356}

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