(x+7)(x+7)=24

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Solution for (x+7)(x+7)=24 equation: 


Simplifying
(x + 7)(x + 7) = 24

Reorder the terms:
(7 + x)(x + 7) = 24

Reorder the terms:
(7 + x)(7 + x) = 24

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = 24
((7 * 7 + x * 7) + x(7 + x)) = 24
((49 + 7x) + x(7 + x)) = 24
(49 + 7x + (7 * x + x * x)) = 24
(49 + 7x + (7x + x2)) = 24

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = 24

Solving
49 + 14x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
49 + -24 + 14x + x2 = 24 + -24

Combine like terms: 49 + -24 = 25
25 + 14x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
25 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 14x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 14x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 14x + x2 = 0 + -25
14x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
14x + x2 = -25

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -25 + 49

Reorder the terms:
49 + 14x + x2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + 14x + x2 = 24

Factor a perfect square on the left side:
(x + 7)(x + 7) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 7) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 7 = 4.898979486

Simplifying
x + 7 = 4.898979486

Reorder the terms:
7 + x = 4.898979486

Solving
7 + x = 4.898979486

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.898979486 + -7
x = 4.898979486 + -7

Combine like terms: 4.898979486 + -7 = -2.101020514
x = -2.101020514

Simplifying
x = -2.101020514


Subproblem 2
x + 7 = -4.898979486

Simplifying
x + 7 = -4.898979486

Reorder the terms:
7 + x = -4.898979486

Solving
7 + x = -4.898979486

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.898979486 + -7
x = -4.898979486 + -7

Combine like terms: -4.898979486 + -7 = -11.898979486
x = -11.898979486

Simplifying
x = -11.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.101020514, -11.898979486}

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