x^2-22x-27=0

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Solution for x^2-22x-27=0 equation:


Simplifying
x2 + -22x + -27 = 0

Reorder the terms:
-27 + -22x + x2 = 0

Solving
-27 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -22x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -22x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -22x + x2 = 0 + 27
-22x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-22x + x2 = 27

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 = 27 + 121

Reorder the terms:
121 + -22x + x2 = 27 + 121

Combine like terms: 27 + 121 = 148
121 + -22x + x2 = 148

Factor a perfect square on the left side:
(x + -11)(x + -11) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + -11) equal to 12.165525061 and -12.165525061.

Subproblem 1

x + -11 = 12.165525061 Simplifying x + -11 = 12.165525061 Reorder the terms: -11 + x = 12.165525061 Solving -11 + x = 12.165525061 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 = 12.165525061 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.165525061 + 11 x = 12.165525061 + 11 Combine like terms: 12.165525061 + 11 = 23.165525061 x = 23.165525061 Simplifying x = 23.165525061

Subproblem 2

x + -11 = -12.165525061 Simplifying x + -11 = -12.165525061 Reorder the terms: -11 + x = -12.165525061 Solving -11 + x = -12.165525061 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 = -12.165525061 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.165525061 + 11 x = -12.165525061 + 11 Combine like terms: -12.165525061 + 11 = -1.165525061 x = -1.165525061 Simplifying x = -1.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.165525061, -1.165525061}

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