8=x(x+16)

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Solution for 8=x(x+16) equation:


Simplifying
8 = x(x + 16)

Reorder the terms:
8 = x(16 + x)
8 = (16 * x + x * x)
8 = (16x + x2)

Solving
8 = 16x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
8 + -16x + -1x2 = 0 + x2 + -1x2
8 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + 16x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 16x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 16x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 16x + x2 = 0 + 8
16x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
16x + x2 = 8

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 8 + 64

Reorder the terms:
64 + 16x + x2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + 16x + x2 = 72

Factor a perfect square on the left side:
(x + 8)(x + 8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 8) equal to 8.485281374 and -8.485281374.

Subproblem 1

x + 8 = 8.485281374 Simplifying x + 8 = 8.485281374 Reorder the terms: 8 + x = 8.485281374 Solving 8 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.485281374 + -8 x = 8.485281374 + -8 Combine like terms: 8.485281374 + -8 = 0.485281374 x = 0.485281374 Simplifying x = 0.485281374

Subproblem 2

x + 8 = -8.485281374 Simplifying x + 8 = -8.485281374 Reorder the terms: 8 + x = -8.485281374 Solving 8 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.485281374 + -8 x = -8.485281374 + -8 Combine like terms: -8.485281374 + -8 = -16.485281374 x = -16.485281374 Simplifying x = -16.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.485281374, -16.485281374}

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