First square both sides of the equation to get: 8x² + 17 = (3x - 2)²
Expand and simplify right side: 8x² + 17 = 9x² - 12x + 4
Rearrange to get: 0 = x² - 12x - 13
Factor to get: 0 = (x - 13)(x + 1)
So, x = 13 or x = -1

IMPORTANT: For square root equations we need to always CHECK for EXTRANEOUS roots by plugging them into the original equation.

x = 13
√[8(13²) + 17] = 3(13) - 2
Simplify to get: √[some big POSITIVE number] = 37
The important thing here is that we are finding the square root of a POSITIVE value, AND the result is also POSITIVE. PERFECT!!
As such, x = 13 is a valid solution


x = -1
√[(8)((-1)²) + 17] = 3(-1) - 2
STOP
When we evaluate the RIGHT side, we get: √[(8)((-1)²) + 17] = -5
The square root of a value cannot equal -5
So, the solution x = -1 is not valid

This means x = 13 is the only valid solution.
Since the question asks for the value of 2x, the correct answer is

Cheers,
Brent

I would have checked x=-1 first since its easier to calculate.

Probably, it's me that I am tired but I cannot understand how sqrt((8)((-1)^2)+17)) could be negative. -1^2 = 1 so we get sqrt(25). Am I wrong?

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