(X+7)X=15

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Solution for (X+7)X=15 equation: 


Simplifying
(X + 7) * X = 15

Reorder the terms:
(7 + X) * X = 15

Reorder the terms for easier multiplication:
X(7 + X) = 15
(7 * X + X * X) = 15
(7X + X2) = 15

Solving
7X + X2 = 15

Solving for variable 'X'.

Reorder the terms:
-15 + 7X + X2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 7X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 7X + 15 + X2 = 0 + 15

Reorder the terms:
-15 + 15 + 7X + X2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7X + X2 = 0 + 15
7X + X2 = 0 + 15

Combine like terms: 0 + 15 = 15
7X + X2 = 15

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 = 15 + 12.25

Reorder the terms:
12.25 + 7X + X2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + 7X + X2 = 27.25

Factor a perfect square on the left side:
(X + 3.5)(X + 3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(X + 3.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
X + 3.5 = 5.220153254

Simplifying
X + 3.5 = 5.220153254

Reorder the terms:
3.5 + X = 5.220153254

Solving
3.5 + X = 5.220153254

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 = 5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + X = 5.220153254 + -3.5
X = 5.220153254 + -3.5

Combine like terms: 5.220153254 + -3.5 = 1.720153254
X = 1.720153254

Simplifying
X = 1.720153254


Subproblem 2
X + 3.5 = -5.220153254

Simplifying
X + 3.5 = -5.220153254

Reorder the terms:
3.5 + X = -5.220153254

Solving
3.5 + X = -5.220153254

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 = -5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + X = -5.220153254 + -3.5
X = -5.220153254 + -3.5

Combine like terms: -5.220153254 + -3.5 = -8.720153254
X = -8.720153254

Simplifying
X = -8.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.720153254, -8.720153254}

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