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 = 9.518284529 X = 9.518284529 Simplifying X = 9.518284529

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 = -31.518284529 X = -31.518284529 Simplifying X = -31.518284529

Solution

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

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