(x-2)(x+4)=36

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Solution for (x-2)(x+4)=36 equation:


Simplifying
(x + -2)(x + 4) = 36

Reorder the terms:
(-2 + x)(x + 4) = 36

Reorder the terms:
(-2 + x)(4 + x) = 36

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) = 36
((4 * -2 + x * -2) + x(4 + x)) = 36
((-8 + -2x) + x(4 + x)) = 36
(-8 + -2x + (4 * x + x * x)) = 36
(-8 + -2x + (4x + x2)) = 36

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2) = 36

Solving
-8 + 2x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
-8 + -36 + 2x + x2 = 36 + -36

Combine like terms: -8 + -36 = -44
-44 + 2x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-44 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 2x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 2x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 2x + x2 = 0 + 44
2x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
2x + x2 = 44

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 = 44 + 1

Reorder the terms:
1 + 2x + x2 = 44 + 1

Combine like terms: 44 + 1 = 45
1 + 2x + x2 = 45

Factor a perfect square on the left side:
(x + 1)(x + 1) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 1) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + 1 = 6.708203933 Simplifying x + 1 = 6.708203933 Reorder the terms: 1 + x = 6.708203933 Solving 1 + x = 6.708203933 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 = 6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.708203933 + -1 x = 6.708203933 + -1 Combine like terms: 6.708203933 + -1 = 5.708203933 x = 5.708203933 Simplifying x = 5.708203933

Subproblem 2

x + 1 = -6.708203933 Simplifying x + 1 = -6.708203933 Reorder the terms: 1 + x = -6.708203933 Solving 1 + x = -6.708203933 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 = -6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.708203933 + -1 x = -6.708203933 + -1 Combine like terms: -6.708203933 + -1 = -7.708203933 x = -7.708203933 Simplifying x = -7.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.708203933, -7.708203933}

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