x^2-110x+750=0

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Solution for x^2-110x+750=0 equation:


Simplifying
x2 + -110x + 750 = 0

Reorder the terms:
750 + -110x + x2 = 0

Solving
750 + -110x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-750' to each side of the equation.
750 + -110x + -750 + x2 = 0 + -750

Reorder the terms:
750 + -750 + -110x + x2 = 0 + -750

Combine like terms: 750 + -750 = 0
0 + -110x + x2 = 0 + -750
-110x + x2 = 0 + -750

Combine like terms: 0 + -750 = -750
-110x + x2 = -750

The x term is -110x.  Take half its coefficient (-55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
-110x + 3025 + x2 = -750 + 3025

Reorder the terms:
3025 + -110x + x2 = -750 + 3025

Combine like terms: -750 + 3025 = 2275
3025 + -110x + x2 = 2275

Factor a perfect square on the left side:
(x + -55)(x + -55) = 2275

Calculate the square root of the right side: 47.696960071

Break this problem into two subproblems by setting 
(x + -55) equal to 47.696960071 and -47.696960071.


Subproblem 1
x + -55 = 47.696960071

Simplifying
x + -55 = 47.696960071

Reorder the terms:
-55 + x = 47.696960071

Solving
-55 + x = 47.696960071

Solving for variable 'x'.

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

Add '55' to each side of the equation.
-55 + 55 + x = 47.696960071 + 55

Combine like terms: -55 + 55 = 0
0 + x = 47.696960071 + 55
x = 47.696960071 + 55

Combine like terms: 47.696960071 + 55 = 102.696960071
x = 102.696960071

Simplifying
x = 102.696960071


Subproblem 2
x + -55 = -47.696960071

Simplifying
x + -55 = -47.696960071

Reorder the terms:
-55 + x = -47.696960071

Solving
-55 + x = -47.696960071

Solving for variable 'x'.

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

Add '55' to each side of the equation.
-55 + 55 + x = -47.696960071 + 55

Combine like terms: -55 + 55 = 0
0 + x = -47.696960071 + 55
x = -47.696960071 + 55

Combine like terms: -47.696960071 + 55 = 7.303039929
x = 7.303039929

Simplifying
x = 7.303039929


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {102.696960071, 7.303039929}

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