(x+7)(x+7)=44

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Solution for (x+7)(x+7)=44 equation:


Simplifying
(x + 7)(x + 7) = 44

Reorder the terms:
(7 + x)(x + 7) = 44

Reorder the terms:
(7 + x)(7 + x) = 44

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = 44
((7 * 7 + x * 7) + x(7 + x)) = 44
((49 + 7x) + x(7 + x)) = 44
(49 + 7x + (7 * x + x * x)) = 44
(49 + 7x + (7x + x2)) = 44

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = 44

Solving
49 + 14x + x2 = 44

Solving for variable 'x'.

Reorder the terms:
49 + -44 + 14x + x2 = 44 + -44

Combine like terms: 49 + -44 = 5
5 + 14x + x2 = 44 + -44

Combine like terms: 44 + -44 = 0
5 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 14x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 14x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 14x + x2 = 0 + -5
14x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
14x + x2 = -5

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 = -5 + 49

Reorder the terms:
49 + 14x + x2 = -5 + 49

Combine like terms: -5 + 49 = 44
49 + 14x + x2 = 44

Factor a perfect square on the left side:
(x + 7)(x + 7) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + 7) equal to 6.633249581 and -6.633249581.

Subproblem 1

x + 7 = 6.633249581 Simplifying x + 7 = 6.633249581 Reorder the terms: 7 + x = 6.633249581 Solving 7 + x = 6.633249581 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 = 6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.633249581 + -7 x = 6.633249581 + -7 Combine like terms: 6.633249581 + -7 = -0.366750419 x = -0.366750419 Simplifying x = -0.366750419

Subproblem 2

x + 7 = -6.633249581 Simplifying x + 7 = -6.633249581 Reorder the terms: 7 + x = -6.633249581 Solving 7 + x = -6.633249581 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 = -6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.633249581 + -7 x = -6.633249581 + -7 Combine like terms: -6.633249581 + -7 = -13.633249581 x = -13.633249581 Simplifying x = -13.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.366750419, -13.633249581}

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