(x-22)(x-22)=12

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Solution for (x-22)(x-22)=12 equation:


Simplifying
(x + -22)(x + -22) = 12

Reorder the terms:
(-22 + x)(x + -22) = 12

Reorder the terms:
(-22 + x)(-22 + x) = 12

Multiply (-22 + x) * (-22 + x)
(-22(-22 + x) + x(-22 + x)) = 12
((-22 * -22 + x * -22) + x(-22 + x)) = 12
((484 + -22x) + x(-22 + x)) = 12
(484 + -22x + (-22 * x + x * x)) = 12
(484 + -22x + (-22x + x2)) = 12

Combine like terms: -22x + -22x = -44x
(484 + -44x + x2) = 12

Solving
484 + -44x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
484 + -12 + -44x + x2 = 12 + -12

Combine like terms: 484 + -12 = 472
472 + -44x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
472 + -44x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-472' to each side of the equation.
472 + -44x + -472 + x2 = 0 + -472

Reorder the terms:
472 + -472 + -44x + x2 = 0 + -472

Combine like terms: 472 + -472 = 0
0 + -44x + x2 = 0 + -472
-44x + x2 = 0 + -472

Combine like terms: 0 + -472 = -472
-44x + x2 = -472

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 = -472 + 484

Reorder the terms:
484 + -44x + x2 = -472 + 484

Combine like terms: -472 + 484 = 12
484 + -44x + x2 = 12

Factor a perfect square on the left side:
(x + -22)(x + -22) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -22) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + -22 = 3.464101615 Simplifying x + -22 = 3.464101615 Reorder the terms: -22 + x = 3.464101615 Solving -22 + x = 3.464101615 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 = 3.464101615 + 22 Combine like terms: -22 + 22 = 0 0 + x = 3.464101615 + 22 x = 3.464101615 + 22 Combine like terms: 3.464101615 + 22 = 25.464101615 x = 25.464101615 Simplifying x = 25.464101615

Subproblem 2

x + -22 = -3.464101615 Simplifying x + -22 = -3.464101615 Reorder the terms: -22 + x = -3.464101615 Solving -22 + x = -3.464101615 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 = -3.464101615 + 22 Combine like terms: -22 + 22 = 0 0 + x = -3.464101615 + 22 x = -3.464101615 + 22 Combine like terms: -3.464101615 + 22 = 18.535898385 x = 18.535898385 Simplifying x = 18.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.464101615, 18.535898385}

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