x^2-22x-300=0

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Solution for x^2-22x-300=0 equation:


Simplifying
x2 + -22x + -300 = 0

Reorder the terms:
-300 + -22x + x2 = 0

Solving
-300 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + -22x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + -22x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + -22x + x2 = 0 + 300
-22x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
-22x + x2 = 300

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 300 + 121

Reorder the terms:
121 + -22x + x2 = 300 + 121

Combine like terms: 300 + 121 = 421
121 + -22x + x2 = 421

Factor a perfect square on the left side:
(x + -11)(x + -11) = 421

Calculate the square root of the right side: 20.518284529

Break this problem into two subproblems by setting 
(x + -11) equal to 20.518284529 and -20.518284529.

Subproblem 1

x + -11 = 20.518284529 Simplifying x + -11 = 20.518284529 Reorder the terms: -11 + x = 20.518284529 Solving -11 + x = 20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 20.518284529 + 11 Combine like terms: -11 + 11 = 0 0 + x = 20.518284529 + 11 x = 20.518284529 + 11 Combine like terms: 20.518284529 + 11 = 31.518284529 x = 31.518284529 Simplifying x = 31.518284529

Subproblem 2

x + -11 = -20.518284529 Simplifying x + -11 = -20.518284529 Reorder the terms: -11 + x = -20.518284529 Solving -11 + x = -20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -20.518284529 + 11 Combine like terms: -11 + 11 = 0 0 + x = -20.518284529 + 11 x = -20.518284529 + 11 Combine like terms: -20.518284529 + 11 = -9.518284529 x = -9.518284529 Simplifying x = -9.518284529

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.518284529, -9.518284529}

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