x(x+8)=7

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Solution for x(x+8)=7 equation: 


Simplifying
x(x + 8) = 7

Reorder the terms:
x(8 + x) = 7
(8 * x + x * x) = 7
(8x + x2) = 7

Solving
8x + x2 = 7

Solving for variable 'x'.

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

Combine like terms: 7 + -7 = 0
-7 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 8x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8x + x2 = 0 + 7
8x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
8x + x2 = 7

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 7 + 16

Reorder the terms:
16 + 8x + x2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + 8x + x2 = 23

Factor a perfect square on the left side:
(x + 4)(x + 4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 4) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + 4 = 4.795831523

Simplifying
x + 4 = 4.795831523

Reorder the terms:
4 + x = 4.795831523

Solving
4 + x = 4.795831523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.795831523 + -4
x = 4.795831523 + -4

Combine like terms: 4.795831523 + -4 = 0.795831523
x = 0.795831523

Simplifying
x = 0.795831523


Subproblem 2
x + 4 = -4.795831523

Simplifying
x + 4 = -4.795831523

Reorder the terms:
4 + x = -4.795831523

Solving
4 + x = -4.795831523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = -4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.795831523 + -4
x = -4.795831523 + -4

Combine like terms: -4.795831523 + -4 = -8.795831523
x = -8.795831523

Simplifying
x = -8.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.795831523, -8.795831523}

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