x^2-22x-820=0

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Solution for x^2-22x-820=0 equation:


Simplifying
x2 + -22x + -820 = 0

Reorder the terms:
-820 + -22x + x2 = 0

Solving
-820 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '820' to each side of the equation.
-820 + -22x + 820 + x2 = 0 + 820

Reorder the terms:
-820 + 820 + -22x + x2 = 0 + 820

Combine like terms: -820 + 820 = 0
0 + -22x + x2 = 0 + 820
-22x + x2 = 0 + 820

Combine like terms: 0 + 820 = 820
-22x + x2 = 820

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 = 820 + 121

Reorder the terms:
121 + -22x + x2 = 820 + 121

Combine like terms: 820 + 121 = 941
121 + -22x + x2 = 941

Factor a perfect square on the left side:
(x + -11)(x + -11) = 941

Calculate the square root of the right side: 30.6757233

Break this problem into two subproblems by setting 
(x + -11) equal to 30.6757233 and -30.6757233.

Subproblem 1

x + -11 = 30.6757233 Simplifying x + -11 = 30.6757233 Reorder the terms: -11 + x = 30.6757233 Solving -11 + x = 30.6757233 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 = 30.6757233 + 11 Combine like terms: -11 + 11 = 0 0 + x = 30.6757233 + 11 x = 30.6757233 + 11 Combine like terms: 30.6757233 + 11 = 41.6757233 x = 41.6757233 Simplifying x = 41.6757233

Subproblem 2

x + -11 = -30.6757233 Simplifying x + -11 = -30.6757233 Reorder the terms: -11 + x = -30.6757233 Solving -11 + x = -30.6757233 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 = -30.6757233 + 11 Combine like terms: -11 + 11 = 0 0 + x = -30.6757233 + 11 x = -30.6757233 + 11 Combine like terms: -30.6757233 + 11 = -19.6757233 x = -19.6757233 Simplifying x = -19.6757233

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.6757233, -19.6757233}

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