x^2-80x+1000=0

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Solution for x^2-80x+1000=0 equation: 


Simplifying
x2 + -80x + 1000 = 0

Reorder the terms:
1000 + -80x + x2 = 0

Solving
1000 + -80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -80x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -80x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -80x + x2 = 0 + -1000
-80x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-80x + x2 = -1000

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -1000 + 1600

Reorder the terms:
1600 + -80x + x2 = -1000 + 1600

Combine like terms: -1000 + 1600 = 600
1600 + -80x + x2 = 600

Factor a perfect square on the left side:
(x + -40)(x + -40) = 600

Calculate the square root of the right side: 24.494897428

Break this problem into two subproblems by setting 
(x + -40) equal to 24.494897428 and -24.494897428.


Subproblem 1
x + -40 = 24.494897428

Simplifying
x + -40 = 24.494897428

Reorder the terms:
-40 + x = 24.494897428

Solving
-40 + x = 24.494897428

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 24.494897428 + 40

Combine like terms: -40 + 40 = 0
0 + x = 24.494897428 + 40
x = 24.494897428 + 40

Combine like terms: 24.494897428 + 40 = 64.494897428
x = 64.494897428

Simplifying
x = 64.494897428


Subproblem 2
x + -40 = -24.494897428

Simplifying
x + -40 = -24.494897428

Reorder the terms:
-40 + x = -24.494897428

Solving
-40 + x = -24.494897428

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -24.494897428 + 40

Combine like terms: -40 + 40 = 0
0 + x = -24.494897428 + 40
x = -24.494897428 + 40

Combine like terms: -24.494897428 + 40 = 15.505102572
x = 15.505102572

Simplifying
x = 15.505102572


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.494897428, 15.505102572}

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