-x^2+150x-1250=0

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Solution for -x^2+150x-1250=0 equation: 


Simplifying
-1x2 + 150x + -1250 = 0

Reorder the terms:
-1250 + 150x + -1x2 = 0

Solving
-1250 + 150x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1250 + -150x + x2 = 0

Move the constant term to the right:

Add '-1250' to each side of the equation.
1250 + -150x + -1250 + x2 = 0 + -1250

Reorder the terms:
1250 + -1250 + -150x + x2 = 0 + -1250

Combine like terms: 1250 + -1250 = 0
0 + -150x + x2 = 0 + -1250
-150x + x2 = 0 + -1250

Combine like terms: 0 + -1250 = -1250
-150x + x2 = -1250

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 = -1250 + 5625

Reorder the terms:
5625 + -150x + x2 = -1250 + 5625

Combine like terms: -1250 + 5625 = 4375
5625 + -150x + x2 = 4375

Factor a perfect square on the left side:
(x + -75)(x + -75) = 4375

Calculate the square root of the right side: 66.143782777

Break this problem into two subproblems by setting 
(x + -75) equal to 66.143782777 and -66.143782777.


Subproblem 1
x + -75 = 66.143782777

Simplifying
x + -75 = 66.143782777

Reorder the terms:
-75 + x = 66.143782777

Solving
-75 + x = 66.143782777

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 = 66.143782777 + 75

Combine like terms: -75 + 75 = 0
0 + x = 66.143782777 + 75
x = 66.143782777 + 75

Combine like terms: 66.143782777 + 75 = 141.143782777
x = 141.143782777

Simplifying
x = 141.143782777


Subproblem 2
x + -75 = -66.143782777

Simplifying
x + -75 = -66.143782777

Reorder the terms:
-75 + x = -66.143782777

Solving
-75 + x = -66.143782777

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 = -66.143782777 + 75

Combine like terms: -75 + 75 = 0
0 + x = -66.143782777 + 75
x = -66.143782777 + 75

Combine like terms: -66.143782777 + 75 = 8.856217223
x = 8.856217223

Simplifying
x = 8.856217223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {141.143782777, 8.856217223}

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