x^2-150x+1000=0

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Solution for x^2-150x+1000=0 equation: 


Simplifying
x2 + -150x + 1000 = 0

Reorder the terms:
1000 + -150x + x2 = 0

Solving
1000 + -150x + 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 + -150x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -150x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -150x + x2 = 0 + -1000
-150x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-150x + x2 = -1000

The x term is -150x.  Take half its coefficient (-75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
-150x + 5625 + x2 = -1000 + 5625

Reorder the terms:
5625 + -150x + x2 = -1000 + 5625

Combine like terms: -1000 + 5625 = 4625
5625 + -150x + x2 = 4625

Factor a perfect square on the left side:
(x + -75)(x + -75) = 4625

Calculate the square root of the right side: 68.007352544

Break this problem into two subproblems by setting 
(x + -75) equal to 68.007352544 and -68.007352544.


Subproblem 1
x + -75 = 68.007352544

Simplifying
x + -75 = 68.007352544

Reorder the terms:
-75 + x = 68.007352544

Solving
-75 + x = 68.007352544

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = 68.007352544 + 75

Combine like terms: -75 + 75 = 0
0 + x = 68.007352544 + 75
x = 68.007352544 + 75

Combine like terms: 68.007352544 + 75 = 143.007352544
x = 143.007352544

Simplifying
x = 143.007352544


Subproblem 2
x + -75 = -68.007352544

Simplifying
x + -75 = -68.007352544

Reorder the terms:
-75 + x = -68.007352544

Solving
-75 + x = -68.007352544

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = -68.007352544 + 75

Combine like terms: -75 + 75 = 0
0 + x = -68.007352544 + 75
x = -68.007352544 + 75

Combine like terms: -68.007352544 + 75 = 6.992647456
x = 6.992647456

Simplifying
x = 6.992647456


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {143.007352544, 6.992647456}

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