(x-18)(x-18)=17

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Solution for (x-18)(x-18)=17 equation:


Simplifying
(x + -18)(x + -18) = 17

Reorder the terms:
(-18 + x)(x + -18) = 17

Reorder the terms:
(-18 + x)(-18 + x) = 17

Multiply (-18 + x) * (-18 + x)
(-18(-18 + x) + x(-18 + x)) = 17
((-18 * -18 + x * -18) + x(-18 + x)) = 17
((324 + -18x) + x(-18 + x)) = 17
(324 + -18x + (-18 * x + x * x)) = 17
(324 + -18x + (-18x + x2)) = 17

Combine like terms: -18x + -18x = -36x
(324 + -36x + x2) = 17

Solving
324 + -36x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
324 + -17 + -36x + x2 = 17 + -17

Combine like terms: 324 + -17 = 307
307 + -36x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
307 + -36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-307' to each side of the equation.
307 + -36x + -307 + x2 = 0 + -307

Reorder the terms:
307 + -307 + -36x + x2 = 0 + -307

Combine like terms: 307 + -307 = 0
0 + -36x + x2 = 0 + -307
-36x + x2 = 0 + -307

Combine like terms: 0 + -307 = -307
-36x + x2 = -307

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -307 + 324

Reorder the terms:
324 + -36x + x2 = -307 + 324

Combine like terms: -307 + 324 = 17
324 + -36x + x2 = 17

Factor a perfect square on the left side:
(x + -18)(x + -18) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -18) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -18 = 4.123105626 Simplifying x + -18 = 4.123105626 Reorder the terms: -18 + x = 4.123105626 Solving -18 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 4.123105626 + 18 Combine like terms: -18 + 18 = 0 0 + x = 4.123105626 + 18 x = 4.123105626 + 18 Combine like terms: 4.123105626 + 18 = 22.123105626 x = 22.123105626 Simplifying x = 22.123105626

Subproblem 2

x + -18 = -4.123105626 Simplifying x + -18 = -4.123105626 Reorder the terms: -18 + x = -4.123105626 Solving -18 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -4.123105626 + 18 Combine like terms: -18 + 18 = 0 0 + x = -4.123105626 + 18 x = -4.123105626 + 18 Combine like terms: -4.123105626 + 18 = 13.876894374 x = 13.876894374 Simplifying x = 13.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.123105626, 13.876894374}

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