(x+4)(x-2)=-2

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


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

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

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

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

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

Solving
-8 + 2x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
-8 + 2 + 2x + x2 = -2 + 2

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 6 + 1

Reorder the terms:
1 + 2x + x2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2x + x2 = 7

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 1 = 2.645751311 Simplifying x + 1 = 2.645751311 Reorder the terms: 1 + x = 2.645751311 Solving 1 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.645751311 + -1 x = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 x = 1.645751311 Simplifying x = 1.645751311

Subproblem 2

x + 1 = -2.645751311 Simplifying x + 1 = -2.645751311 Reorder the terms: 1 + x = -2.645751311 Solving 1 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.645751311 + -1 x = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 x = -3.645751311 Simplifying x = -3.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.645751311, -3.645751311}

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