.5x(x+8)=45

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Solution for .5x(x+8)=45 equation: 


Simplifying
0.5x(x + 8) = 45

Reorder the terms:
0.5x(8 + x) = 45
(8 * 0.5x + x * 0.5x) = 45
(4x + 0.5x2) = 45

Solving
4x + 0.5x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 4x + 0.5x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 4x + 0.5x2 = 0

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

Divide each side by '0.5'.
-90 + 8x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 8x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 8x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 8x + x2 = 0 + 90
8x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
8x + x2 = 90

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 = 90 + 16

Reorder the terms:
16 + 8x + x2 = 90 + 16

Combine like terms: 90 + 16 = 106
16 + 8x + x2 = 106

Factor a perfect square on the left side:
(x + 4)(x + 4) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 4) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + 4 = 10.295630141

Simplifying
x + 4 = 10.295630141

Reorder the terms:
4 + x = 10.295630141

Solving
4 + x = 10.295630141

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 = 10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + x = 10.295630141 + -4
x = 10.295630141 + -4

Combine like terms: 10.295630141 + -4 = 6.295630141
x = 6.295630141

Simplifying
x = 6.295630141


Subproblem 2
x + 4 = -10.295630141

Simplifying
x + 4 = -10.295630141

Reorder the terms:
4 + x = -10.295630141

Solving
4 + x = -10.295630141

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 = -10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + x = -10.295630141 + -4
x = -10.295630141 + -4

Combine like terms: -10.295630141 + -4 = -14.295630141
x = -14.295630141

Simplifying
x = -14.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.295630141, -14.295630141}

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