(x+15)(x+15)+5=50

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Solution for (x+15)(x+15)+5=50 equation: 


Simplifying
(x + 15)(x + 15) + 5 = 50

Reorder the terms:
(15 + x)(x + 15) + 5 = 50

Reorder the terms:
(15 + x)(15 + x) + 5 = 50

Multiply (15 + x) * (15 + x)
(15(15 + x) + x(15 + x)) + 5 = 50
((15 * 15 + x * 15) + x(15 + x)) + 5 = 50
((225 + 15x) + x(15 + x)) + 5 = 50
(225 + 15x + (15 * x + x * x)) + 5 = 50
(225 + 15x + (15x + x2)) + 5 = 50

Combine like terms: 15x + 15x = 30x
(225 + 30x + x2) + 5 = 50

Reorder the terms:
225 + 5 + 30x + x2 = 50

Combine like terms: 225 + 5 = 230
230 + 30x + x2 = 50

Solving
230 + 30x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
230 + -50 + 30x + x2 = 50 + -50

Combine like terms: 230 + -50 = 180
180 + 30x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
180 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + 30x + -180 + x2 = 0 + -180

Reorder the terms:
180 + -180 + 30x + x2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + 30x + x2 = 0 + -180
30x + x2 = 0 + -180

Combine like terms: 0 + -180 = -180
30x + x2 = -180

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -180 + 225

Reorder the terms:
225 + 30x + x2 = -180 + 225

Combine like terms: -180 + 225 = 45
225 + 30x + x2 = 45

Factor a perfect square on the left side:
(x + 15)(x + 15) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 15) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 15 = 6.708203933

Simplifying
x + 15 = 6.708203933

Reorder the terms:
15 + x = 6.708203933

Solving
15 + x = 6.708203933

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 6.708203933 + -15

Combine like terms: 15 + -15 = 0
0 + x = 6.708203933 + -15
x = 6.708203933 + -15

Combine like terms: 6.708203933 + -15 = -8.291796067
x = -8.291796067

Simplifying
x = -8.291796067


Subproblem 2
x + 15 = -6.708203933

Simplifying
x + 15 = -6.708203933

Reorder the terms:
15 + x = -6.708203933

Solving
15 + x = -6.708203933

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -6.708203933 + -15

Combine like terms: 15 + -15 = 0
0 + x = -6.708203933 + -15
x = -6.708203933 + -15

Combine like terms: -6.708203933 + -15 = -21.708203933
x = -21.708203933

Simplifying
x = -21.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.291796067, -21.708203933}

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