x^2-4x=22

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Solution for x^2-4x=22 equation:


Simplifying
x2 + -4x = 22

Reorder the terms:
-4x + x2 = 22

Solving
-4x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + -4x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -4x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -4x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -4x + x2 = 0 + 22
-4x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-4x + x2 = 22

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 22 + 4

Reorder the terms:
4 + -4x + x2 = 22 + 4

Combine like terms: 22 + 4 = 26
4 + -4x + x2 = 26

Factor a perfect square on the left side:
(x + -2)(x + -2) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -2) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + -2 = 5.099019514 Simplifying x + -2 = 5.099019514 Reorder the terms: -2 + x = 5.099019514 Solving -2 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.099019514 + 2 x = 5.099019514 + 2 Combine like terms: 5.099019514 + 2 = 7.099019514 x = 7.099019514 Simplifying x = 7.099019514

Subproblem 2

x + -2 = -5.099019514 Simplifying x + -2 = -5.099019514 Reorder the terms: -2 + x = -5.099019514 Solving -2 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.099019514 + 2 x = -5.099019514 + 2 Combine like terms: -5.099019514 + 2 = -3.099019514 x = -3.099019514 Simplifying x = -3.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.099019514, -3.099019514}

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