x+(x+2)(x+4)=392

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Solution for x+(x+2)(x+4)=392 equation:


Simplifying
x + (x + 2)(x + 4) = 392

Reorder the terms:
x + (2 + x)(x + 4) = 392

Reorder the terms:
x + (2 + x)(4 + x) = 392

Multiply (2 + x) * (4 + x)
x + (2(4 + x) + x(4 + x)) = 392
x + ((4 * 2 + x * 2) + x(4 + x)) = 392
x + ((8 + 2x) + x(4 + x)) = 392
x + (8 + 2x + (4 * x + x * x)) = 392
x + (8 + 2x + (4x + x2)) = 392

Combine like terms: 2x + 4x = 6x
x + (8 + 6x + x2) = 392

Reorder the terms:
8 + x + 6x + x2 = 392

Combine like terms: x + 6x = 7x
8 + 7x + x2 = 392

Solving
8 + 7x + x2 = 392

Solving for variable 'x'.

Reorder the terms:
8 + -392 + 7x + x2 = 392 + -392

Combine like terms: 8 + -392 = -384
-384 + 7x + x2 = 392 + -392

Combine like terms: 392 + -392 = 0
-384 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '384' to each side of the equation.
-384 + 7x + 384 + x2 = 0 + 384

Reorder the terms:
-384 + 384 + 7x + x2 = 0 + 384

Combine like terms: -384 + 384 = 0
0 + 7x + x2 = 0 + 384
7x + x2 = 0 + 384

Combine like terms: 0 + 384 = 384
7x + x2 = 384

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 384 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 384 + 12.25

Combine like terms: 384 + 12.25 = 396.25
12.25 + 7x + x2 = 396.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 396.25

Calculate the square root of the right side: 19.906029237

Break this problem into two subproblems by setting 
(x + 3.5) equal to 19.906029237 and -19.906029237.

Subproblem 1

x + 3.5 = 19.906029237 Simplifying x + 3.5 = 19.906029237 Reorder the terms: 3.5 + x = 19.906029237 Solving 3.5 + x = 19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 19.906029237 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 19.906029237 + -3.5 x = 19.906029237 + -3.5 Combine like terms: 19.906029237 + -3.5 = 16.406029237 x = 16.406029237 Simplifying x = 16.406029237

Subproblem 2

x + 3.5 = -19.906029237 Simplifying x + 3.5 = -19.906029237 Reorder the terms: 3.5 + x = -19.906029237 Solving 3.5 + x = -19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -19.906029237 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -19.906029237 + -3.5 x = -19.906029237 + -3.5 Combine like terms: -19.906029237 + -3.5 = -23.406029237 x = -23.406029237 Simplifying x = -23.406029237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.406029237, -23.406029237}

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