(x+2)(x+4)=10000

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Solution for (x+2)(x+4)=10000 equation:


Simplifying
(x + 2)(x + 4) = 10000

Reorder the terms:
(2 + x)(x + 4) = 10000

Reorder the terms:
(2 + x)(4 + x) = 10000

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = 10000
((4 * 2 + x * 2) + x(4 + x)) = 10000
((8 + 2x) + x(4 + x)) = 10000
(8 + 2x + (4 * x + x * x)) = 10000
(8 + 2x + (4x + x2)) = 10000

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = 10000

Solving
8 + 6x + x2 = 10000

Solving for variable 'x'.

Reorder the terms:
8 + -10000 + 6x + x2 = 10000 + -10000

Combine like terms: 8 + -10000 = -9992
-9992 + 6x + x2 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-9992 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9992' to each side of the equation.
-9992 + 6x + 9992 + x2 = 0 + 9992

Reorder the terms:
-9992 + 9992 + 6x + x2 = 0 + 9992

Combine like terms: -9992 + 9992 = 0
0 + 6x + x2 = 0 + 9992
6x + x2 = 0 + 9992

Combine like terms: 0 + 9992 = 9992
6x + x2 = 9992

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 = 9992 + 9

Reorder the terms:
9 + 6x + x2 = 9992 + 9

Combine like terms: 9992 + 9 = 10001
9 + 6x + x2 = 10001

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10001

Calculate the square root of the right side: 100.004999875

Break this problem into two subproblems by setting 
(x + 3) equal to 100.004999875 and -100.004999875.

Subproblem 1

x + 3 = 100.004999875 Simplifying x + 3 = 100.004999875 Reorder the terms: 3 + x = 100.004999875 Solving 3 + x = 100.004999875 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 = 100.004999875 + -3 Combine like terms: 3 + -3 = 0 0 + x = 100.004999875 + -3 x = 100.004999875 + -3 Combine like terms: 100.004999875 + -3 = 97.004999875 x = 97.004999875 Simplifying x = 97.004999875

Subproblem 2

x + 3 = -100.004999875 Simplifying x + 3 = -100.004999875 Reorder the terms: 3 + x = -100.004999875 Solving 3 + x = -100.004999875 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 = -100.004999875 + -3 Combine like terms: 3 + -3 = 0 0 + x = -100.004999875 + -3 x = -100.004999875 + -3 Combine like terms: -100.004999875 + -3 = -103.004999875 x = -103.004999875 Simplifying x = -103.004999875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {97.004999875, -103.004999875}

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