x^2-110x+400=0

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Solution for x^2-110x+400=0 equation:


Simplifying
x2 + -110x + 400 = 0

Reorder the terms:
400 + -110x + x2 = 0

Solving
400 + -110x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-400' to each side of the equation.
400 + -110x + -400 + x2 = 0 + -400

Reorder the terms:
400 + -400 + -110x + x2 = 0 + -400

Combine like terms: 400 + -400 = 0
0 + -110x + x2 = 0 + -400
-110x + x2 = 0 + -400

Combine like terms: 0 + -400 = -400
-110x + x2 = -400

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 = -400 + 3025

Reorder the terms:
3025 + -110x + x2 = -400 + 3025

Combine like terms: -400 + 3025 = 2625
3025 + -110x + x2 = 2625

Factor a perfect square on the left side:
(x + -55)(x + -55) = 2625

Calculate the square root of the right side: 51.23475383

Break this problem into two subproblems by setting 
(x + -55) equal to 51.23475383 and -51.23475383.

Subproblem 1

x + -55 = 51.23475383 Simplifying x + -55 = 51.23475383 Reorder the terms: -55 + x = 51.23475383 Solving -55 + x = 51.23475383 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 = 51.23475383 + 55 Combine like terms: -55 + 55 = 0 0 + x = 51.23475383 + 55 x = 51.23475383 + 55 Combine like terms: 51.23475383 + 55 = 106.23475383 x = 106.23475383 Simplifying x = 106.23475383

Subproblem 2

x + -55 = -51.23475383 Simplifying x + -55 = -51.23475383 Reorder the terms: -55 + x = -51.23475383 Solving -55 + x = -51.23475383 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 = -51.23475383 + 55 Combine like terms: -55 + 55 = 0 0 + x = -51.23475383 + 55 x = -51.23475383 + 55 Combine like terms: -51.23475383 + 55 = 3.76524617 x = 3.76524617 Simplifying x = 3.76524617

Solution

The solution to the problem is based on the solutions from the subproblems. x = {106.23475383, 3.76524617}

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