x^2-22x-94=0

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Solution for x^2-22x-94=0 equation:


Simplifying
x2 + -22x + -94 = 0

Reorder the terms:
-94 + -22x + x2 = 0

Solving
-94 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '94' to each side of the equation.
-94 + -22x + 94 + x2 = 0 + 94

Reorder the terms:
-94 + 94 + -22x + x2 = 0 + 94

Combine like terms: -94 + 94 = 0
0 + -22x + x2 = 0 + 94
-22x + x2 = 0 + 94

Combine like terms: 0 + 94 = 94
-22x + x2 = 94

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 = 94 + 121

Reorder the terms:
121 + -22x + x2 = 94 + 121

Combine like terms: 94 + 121 = 215
121 + -22x + x2 = 215

Factor a perfect square on the left side:
(x + -11)(x + -11) = 215

Calculate the square root of the right side: 14.662878299

Break this problem into two subproblems by setting 
(x + -11) equal to 14.662878299 and -14.662878299.

Subproblem 1

x + -11 = 14.662878299 Simplifying x + -11 = 14.662878299 Reorder the terms: -11 + x = 14.662878299 Solving -11 + x = 14.662878299 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 = 14.662878299 + 11 Combine like terms: -11 + 11 = 0 0 + x = 14.662878299 + 11 x = 14.662878299 + 11 Combine like terms: 14.662878299 + 11 = 25.662878299 x = 25.662878299 Simplifying x = 25.662878299

Subproblem 2

x + -11 = -14.662878299 Simplifying x + -11 = -14.662878299 Reorder the terms: -11 + x = -14.662878299 Solving -11 + x = -14.662878299 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 = -14.662878299 + 11 Combine like terms: -11 + 11 = 0 0 + x = -14.662878299 + 11 x = -14.662878299 + 11 Combine like terms: -14.662878299 + 11 = -3.662878299 x = -3.662878299 Simplifying x = -3.662878299

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.662878299, -3.662878299}

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