(x-22)(x-22)=18

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Solution for (x-22)(x-22)=18 equation:


Simplifying
(x + -22)(x + -22) = 18

Reorder the terms:
(-22 + x)(x + -22) = 18

Reorder the terms:
(-22 + x)(-22 + x) = 18

Multiply (-22 + x) * (-22 + x)
(-22(-22 + x) + x(-22 + x)) = 18
((-22 * -22 + x * -22) + x(-22 + x)) = 18
((484 + -22x) + x(-22 + x)) = 18
(484 + -22x + (-22 * x + x * x)) = 18
(484 + -22x + (-22x + x2)) = 18

Combine like terms: -22x + -22x = -44x
(484 + -44x + x2) = 18

Solving
484 + -44x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
484 + -18 + -44x + x2 = 18 + -18

Combine like terms: 484 + -18 = 466
466 + -44x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
466 + -44x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-466' to each side of the equation.
466 + -44x + -466 + x2 = 0 + -466

Reorder the terms:
466 + -466 + -44x + x2 = 0 + -466

Combine like terms: 466 + -466 = 0
0 + -44x + x2 = 0 + -466
-44x + x2 = 0 + -466

Combine like terms: 0 + -466 = -466
-44x + x2 = -466

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -466 + 484

Reorder the terms:
484 + -44x + x2 = -466 + 484

Combine like terms: -466 + 484 = 18
484 + -44x + x2 = 18

Factor a perfect square on the left side:
(x + -22)(x + -22) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -22) equal to 4.242640687 and -4.242640687.

Subproblem 1

x + -22 = 4.242640687 Simplifying x + -22 = 4.242640687 Reorder the terms: -22 + x = 4.242640687 Solving -22 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 4.242640687 + 22 Combine like terms: -22 + 22 = 0 0 + x = 4.242640687 + 22 x = 4.242640687 + 22 Combine like terms: 4.242640687 + 22 = 26.242640687 x = 26.242640687 Simplifying x = 26.242640687

Subproblem 2

x + -22 = -4.242640687 Simplifying x + -22 = -4.242640687 Reorder the terms: -22 + x = -4.242640687 Solving -22 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -4.242640687 + 22 Combine like terms: -22 + 22 = 0 0 + x = -4.242640687 + 22 x = -4.242640687 + 22 Combine like terms: -4.242640687 + 22 = 17.757359313 x = 17.757359313 Simplifying x = 17.757359313

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.242640687, 17.757359313}

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