(x+4)(x+2)=10

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Solution for (x+4)(x+2)=10 equation:


Simplifying
(x + 4)(x + 2) = 10

Reorder the terms:
(4 + x)(x + 2) = 10

Reorder the terms:
(4 + x)(2 + x) = 10

Multiply (4 + x) * (2 + x)
(4(2 + x) + x(2 + x)) = 10
((2 * 4 + x * 4) + x(2 + x)) = 10
((8 + 4x) + x(2 + x)) = 10
(8 + 4x + (2 * x + x * x)) = 10
(8 + 4x + (2x + x2)) = 10

Combine like terms: 4x + 2x = 6x
(8 + 6x + x2) = 10

Solving
8 + 6x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
8 + -10 + 6x + x2 = 10 + -10

Combine like terms: 8 + -10 = -2
-2 + 6x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-2 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6x + x2 = 0 + 2
6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
6x + x2 = 2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 2 + 9

Reorder the terms:
9 + 6x + x2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6x + x2 = 11

Factor a perfect square on the left side:
(x + 3)(x + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 3) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479

Subproblem 2

x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}

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