0.8x^2-24x-320=

Solution for 0.8x^2-24x-320= equation:

Simplifying
0.8x2 + -24x + -320 = 0

Reorder the terms:
-320 + -24x + 0.8x2 = 0

Solving
-320 + -24x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
-400 + -30x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -30x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -30x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -30x + x2 = 0 + 400
-30x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-30x + x2 = 400

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 400 + 225

Reorder the terms:
225 + -30x + x2 = 400 + 225

Combine like terms: 400 + 225 = 625
225 + -30x + x2 = 625

Factor a perfect square on the left side:
(x + -15)(x + -15) = 625

Calculate the square root of the right side: 25

Break this problem into two subproblems by setting 
(x + -15) equal to 25 and -25.

Subproblem 1
x + -15 = 25

Simplifying
x + -15 = 25

Reorder the terms:
-15 + x = 25

Solving
-15 + x = 25

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 25 + 15

Combine like terms: -15 + 15 = 0
0 + x = 25 + 15
x = 25 + 15

Combine like terms: 25 + 15 = 40
x = 40

Simplifying
x = 40

Subproblem 2
x + -15 = -25

Simplifying
x + -15 = -25

Reorder the terms:
-15 + x = -25

Solving
-15 + x = -25

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -25 + 15

Combine like terms: -15 + 15 = 0
0 + x = -25 + 15
x = -25 + 15

Combine like terms: -25 + 15 = -10
x = -10

Simplifying
x = -10

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40, -10}