(x-17)(x-17)=8

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Solution for (x-17)(x-17)=8 equation:


Simplifying
(x + -17)(x + -17) = 8

Reorder the terms:
(-17 + x)(x + -17) = 8

Reorder the terms:
(-17 + x)(-17 + x) = 8

Multiply (-17 + x) * (-17 + x)
(-17(-17 + x) + x(-17 + x)) = 8
((-17 * -17 + x * -17) + x(-17 + x)) = 8
((289 + -17x) + x(-17 + x)) = 8
(289 + -17x + (-17 * x + x * x)) = 8
(289 + -17x + (-17x + x2)) = 8

Combine like terms: -17x + -17x = -34x
(289 + -34x + x2) = 8

Solving
289 + -34x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
289 + -8 + -34x + x2 = 8 + -8

Combine like terms: 289 + -8 = 281
281 + -34x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
281 + -34x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-281' to each side of the equation.
281 + -34x + -281 + x2 = 0 + -281

Reorder the terms:
281 + -281 + -34x + x2 = 0 + -281

Combine like terms: 281 + -281 = 0
0 + -34x + x2 = 0 + -281
-34x + x2 = 0 + -281

Combine like terms: 0 + -281 = -281
-34x + x2 = -281

The x term is -34x.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x + 289 + x2 = -281 + 289

Reorder the terms:
289 + -34x + x2 = -281 + 289

Combine like terms: -281 + 289 = 8
289 + -34x + x2 = 8

Factor a perfect square on the left side:
(x + -17)(x + -17) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -17) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -17 = 2.828427125 Simplifying x + -17 = 2.828427125 Reorder the terms: -17 + x = 2.828427125 Solving -17 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 2.828427125 + 17 Combine like terms: -17 + 17 = 0 0 + x = 2.828427125 + 17 x = 2.828427125 + 17 Combine like terms: 2.828427125 + 17 = 19.828427125 x = 19.828427125 Simplifying x = 19.828427125

Subproblem 2

x + -17 = -2.828427125 Simplifying x + -17 = -2.828427125 Reorder the terms: -17 + x = -2.828427125 Solving -17 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -2.828427125 + 17 Combine like terms: -17 + 17 = 0 0 + x = -2.828427125 + 17 x = -2.828427125 + 17 Combine like terms: -2.828427125 + 17 = 14.171572875 x = 14.171572875 Simplifying x = 14.171572875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.828427125, 14.171572875}

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