(x+6)(x+4)=6

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Solution for (x+6)(x+4)=6 equation:


Simplifying
(x + 6)(x + 4) = 6

Reorder the terms:
(6 + x)(x + 4) = 6

Reorder the terms:
(6 + x)(4 + x) = 6

Multiply (6 + x) * (4 + x)
(6(4 + x) + x(4 + x)) = 6
((4 * 6 + x * 6) + x(4 + x)) = 6
((24 + 6x) + x(4 + x)) = 6
(24 + 6x + (4 * x + x * x)) = 6
(24 + 6x + (4x + x2)) = 6

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = 6

Solving
24 + 10x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
24 + -6 + 10x + x2 = 6 + -6

Combine like terms: 24 + -6 = 18
18 + 10x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
18 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 10x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10x + x2 = 0 + -18
10x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
10x + x2 = -18

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -18 + 25

Reorder the terms:
25 + 10x + x2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10x + x2 = 7

Factor a perfect square on the left side:
(x + 5)(x + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 5) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 5 = 2.645751311 Simplifying x + 5 = 2.645751311 Reorder the terms: 5 + x = 2.645751311 Solving 5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.645751311 + -5 x = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 x = -2.354248689 Simplifying x = -2.354248689

Subproblem 2

x + 5 = -2.645751311 Simplifying x + 5 = -2.645751311 Reorder the terms: 5 + x = -2.645751311 Solving 5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.645751311 + -5 x = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 x = -7.645751311 Simplifying x = -7.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.354248689, -7.645751311}

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