x*5(x+7)=215

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Solution for x*5(x+7)=215 equation: 


Simplifying
x * 5(x + 7) = 215

Reorder the terms:
x * 5(7 + x) = 215

Reorder the terms for easier multiplication:
5x(7 + x) = 215
(7 * 5x + x * 5x) = 215
(35x + 5x2) = 215

Solving
35x + 5x2 = 215

Solving for variable 'x'.

Reorder the terms:
-215 + 35x + 5x2 = 215 + -215

Combine like terms: 215 + -215 = 0
-215 + 35x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-43 + 7x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-43 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-43 + 7x + x2 = 0

Solving
-43 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 7x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + 7x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 7x + x2 = 0 + 43
7x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
7x + x2 = 43

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 43 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 43 + 12.25

Combine like terms: 43 + 12.25 = 55.25
12.25 + 7x + x2 = 55.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.433034374 and -7.433034374.


Subproblem 1
x + 3.5 = 7.433034374

Simplifying
x + 3.5 = 7.433034374

Reorder the terms:
3.5 + x = 7.433034374

Solving
3.5 + x = 7.433034374

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 7.433034374 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.433034374 + -3.5
x = 7.433034374 + -3.5

Combine like terms: 7.433034374 + -3.5 = 3.933034374
x = 3.933034374

Simplifying
x = 3.933034374


Subproblem 2
x + 3.5 = -7.433034374

Simplifying
x + 3.5 = -7.433034374

Reorder the terms:
3.5 + x = -7.433034374

Solving
3.5 + x = -7.433034374

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -7.433034374 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.433034374 + -3.5
x = -7.433034374 + -3.5

Combine like terms: -7.433034374 + -3.5 = -10.933034374
x = -10.933034374

Simplifying
x = -10.933034374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.933034374, -10.933034374}
Solution
x = {3.933034374, -10.933034374}

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