x^2-22x-54=0

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Solution for x^2-22x-54=0 equation:


Simplifying
x2 + -22x + -54 = 0

Reorder the terms:
-54 + -22x + x2 = 0

Solving
-54 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -22x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -22x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -22x + x2 = 0 + 54
-22x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-22x + x2 = 54

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 = 54 + 121

Reorder the terms:
121 + -22x + x2 = 54 + 121

Combine like terms: 54 + 121 = 175
121 + -22x + x2 = 175

Factor a perfect square on the left side:
(x + -11)(x + -11) = 175

Calculate the square root of the right side: 13.228756555

Break this problem into two subproblems by setting 
(x + -11) equal to 13.228756555 and -13.228756555.

Subproblem 1

x + -11 = 13.228756555 Simplifying x + -11 = 13.228756555 Reorder the terms: -11 + x = 13.228756555 Solving -11 + x = 13.228756555 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 = 13.228756555 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.228756555 + 11 x = 13.228756555 + 11 Combine like terms: 13.228756555 + 11 = 24.228756555 x = 24.228756555 Simplifying x = 24.228756555

Subproblem 2

x + -11 = -13.228756555 Simplifying x + -11 = -13.228756555 Reorder the terms: -11 + x = -13.228756555 Solving -11 + x = -13.228756555 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 = -13.228756555 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.228756555 + 11 x = -13.228756555 + 11 Combine like terms: -13.228756555 + 11 = -2.228756555 x = -2.228756555 Simplifying x = -2.228756555

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.228756555, -2.228756555}

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