(x-2)^2 = 45, solve for x?

(x - 2)^2 = 45

x = 2 ± 3√5

QED

(x - 2)^2 = 45

Take the square root of both sides.

(IMPORTANT: The square root property states that, when taking the root of both sides, we must include both positive and negative solutions).

x - 2 = +/- sqrt(45)

sqrt(45) = sqrt(9*5) = 3sqrt(5), so

x - 2 = +/- 3sqrt(5), so

x = 2 +/- 3sqrt(5)

Making the solutions

x = { 2 + 3sqrt(5) , 2 - 3sqrt(5) }

x-2=+-√ 45

x-2=+-3√ 5

x=2+-3√ 5

Take the square root of both sides. When you take the square root of 45, it will need to write + and - the square root as you don't know which one it will be. Then add the two to both sides. You end up with

x = 2 +/- sqrt(45), sqrt(45) will reduce to sqrt(9*5) which will reduce down to 3sqrt(5).

Final answer will be:

x=+/- 3sqrt(5)

(x-2)^2 = 45 is equal to

(x-2)(x-2) = 45

which is equal to

x^2 - 2x - 2x + 4 = 45

which you can combine to get

x^2 - 4x + 4 = 45

which you can make a quadratic

x^2 - 4x - 41 = 0

which you can factor.

bada-bing, bada-boom, you have x.

(x-2)^2=45

x^2-4=45

x^2=49

x=7