(5x+15)(5x+15)=200

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Solution for (5x+15)(5x+15)=200 equation: 


Simplifying
(5x + 15)(5x + 15) = 200

Reorder the terms:
(15 + 5x)(5x + 15) = 200

Reorder the terms:
(15 + 5x)(15 + 5x) = 200

Multiply (15 + 5x) * (15 + 5x)
(15(15 + 5x) + 5x * (15 + 5x)) = 200
((15 * 15 + 5x * 15) + 5x * (15 + 5x)) = 200
((225 + 75x) + 5x * (15 + 5x)) = 200
(225 + 75x + (15 * 5x + 5x * 5x)) = 200
(225 + 75x + (75x + 25x2)) = 200

Combine like terms: 75x + 75x = 150x
(225 + 150x + 25x2) = 200

Solving
225 + 150x + 25x2 = 200

Solving for variable 'x'.

Reorder the terms:
225 + -200 + 150x + 25x2 = 200 + -200

Combine like terms: 225 + -200 = 25
25 + 150x + 25x2 = 200 + -200

Combine like terms: 200 + -200 = 0
25 + 150x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(1 + 6x + x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(1 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 6x + x2 = 0

Solving
1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 6x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 6x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x + x2 = 0 + -1
6x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
6x + x2 = -1

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1 + 9

Reorder the terms:
9 + 6x + x2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + 6x + x2 = 8

Factor a perfect square on the left side:
(x + 3)(x + 3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 3) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 3 = 2.828427125

Simplifying
x + 3 = 2.828427125

Reorder the terms:
3 + x = 2.828427125

Solving
3 + x = 2.828427125

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.828427125 + -3
x = 2.828427125 + -3

Combine like terms: 2.828427125 + -3 = -0.171572875
x = -0.171572875

Simplifying
x = -0.171572875


Subproblem 2
x + 3 = -2.828427125

Simplifying
x + 3 = -2.828427125

Reorder the terms:
3 + x = -2.828427125

Solving
3 + x = -2.828427125

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.828427125 + -3
x = -2.828427125 + -3

Combine like terms: -2.828427125 + -3 = -5.828427125
x = -5.828427125

Simplifying
x = -5.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.171572875, -5.828427125}
Solution
x = {-0.171572875, -5.828427125}

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