x(x+8)=(x+4)2

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Solution for x(x+8)=(x+4)2 equation:


Simplifying
x(x + 8) = (x + 4) * 2

Reorder the terms:
x(8 + x) = (x + 4) * 2
(8 * x + x * x) = (x + 4) * 2
(8x + x2) = (x + 4) * 2

Reorder the terms:
8x + x2 = (4 + x) * 2

Reorder the terms for easier multiplication:
8x + x2 = 2(4 + x)
8x + x2 = (4 * 2 + x * 2)
8x + x2 = (8 + 2x)

Solving
8x + x2 = 8 + 2x

Solving for variable 'x'.

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

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

Reorder the terms:
-8 + 6x + x2 = 8 + -8 + 2x + -2x

Combine like terms: 8 + -8 = 0
-8 + 6x + x2 = 0 + 2x + -2x
-8 + 6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-8 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6x + x2 = 0 + 8
6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
6x + x2 = 8

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 = 8 + 9

Reorder the terms:
9 + 6x + x2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + 6x + x2 = 17

Factor a perfect square on the left side:
(x + 3)(x + 3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 3) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + 3 = 4.123105626 Simplifying x + 3 = 4.123105626 Reorder the terms: 3 + x = 4.123105626 Solving 3 + x = 4.123105626 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.123105626 + -3 x = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 x = 1.123105626 Simplifying x = 1.123105626

Subproblem 2

x + 3 = -4.123105626 Simplifying x + 3 = -4.123105626 Reorder the terms: 3 + x = -4.123105626 Solving 3 + x = -4.123105626 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.123105626 + -3 x = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 x = -7.123105626 Simplifying x = -7.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.123105626, -7.123105626}

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