(x+8)*(2.5x-16)=

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Solution for (x+8)*(2.5x-16)= equation: 


Simplifying
(x + 8)(2.5x + -16) = 0

Reorder the terms:
(8 + x)(2.5x + -16) = 0

Reorder the terms:
(8 + x)(-16 + 2.5x) = 0

Multiply (8 + x) * (-16 + 2.5x)
(8(-16 + 2.5x) + x(-16 + 2.5x)) = 0
((-16 * 8 + 2.5x * 8) + x(-16 + 2.5x)) = 0
((-128 + 20x) + x(-16 + 2.5x)) = 0
(-128 + 20x + (-16 * x + 2.5x * x)) = 0
(-128 + 20x + (-16x + 2.5x2)) = 0

Combine like terms: 20x + -16x = 4x
(-128 + 4x + 2.5x2) = 0

Solving
-128 + 4x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-51.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '51.2' to each side of the equation.
-51.2 + 1.6x + 51.2 + x2 = 0 + 51.2

Reorder the terms:
-51.2 + 51.2 + 1.6x + x2 = 0 + 51.2

Combine like terms: -51.2 + 51.2 = 0.0
0.0 + 1.6x + x2 = 0 + 51.2
1.6x + x2 = 0 + 51.2

Combine like terms: 0 + 51.2 = 51.2
1.6x + x2 = 51.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 51.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 51.2 + 0.64

Combine like terms: 51.2 + 0.64 = 51.84
0.64 + 1.6x + x2 = 51.84

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 51.84

Calculate the square root of the right side: 7.2

Break this problem into two subproblems by setting 
(x + 0.8) equal to 7.2 and -7.2.


Subproblem 1
x + 0.8 = 7.2

Simplifying
x + 0.8 = 7.2

Reorder the terms:
0.8 + x = 7.2

Solving
0.8 + x = 7.2

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 7.2 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 7.2 + -0.8
x = 7.2 + -0.8

Combine like terms: 7.2 + -0.8 = 6.4
x = 6.4

Simplifying
x = 6.4


Subproblem 2
x + 0.8 = -7.2

Simplifying
x + 0.8 = -7.2

Reorder the terms:
0.8 + x = -7.2

Solving
0.8 + x = -7.2

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -7.2 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -7.2 + -0.8
x = -7.2 + -0.8

Combine like terms: -7.2 + -0.8 = -8
x = -8

Simplifying
x = -8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.4, -8}

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