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How do you solve #7(x-4)^2-2=54# using any method?

Answer 1

Abigail Allen

#x=4+-2sqrt2#

#7(x-4)^2=56# #(x-4)^2=8# #x-4=+-2sqrt2# #x=4+-2sqrt2#

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Answer 2

Ethan Adkins

#x=4+-2sqrt2#

#color(blue)"Isolate " (x-4)^2" on the left side"#

#"add 2 to each side"#

#7(x-4)^2cancel(-2)cancel(+2)=54+2#

#rArr7(x-4)^2=56#

#"divide both sides by 7"#

#(cancel(7)(x-4)^2)/cancel(7)=56/7#

#rArr(x-4)^2=8#

#color(blue)"take the square root of both sides"#

#sqrt((x-4)^2)=+-sqrt8rarr(sqrt8=sqrt(4xx2))#

#rArrx-4=+-2sqrt2#

#rArrx=4+-2sqrt2#

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Answer 3

Isaiah Anthony

To solve the equation 7(x-4)^2 - 2 = 54:

Add 2 to both sides: 7(x-4)^2 = 56
Divide both sides by 7: (x-4)^2 = 8
Take the square root of both sides: x - 4 = ±√8
Add 4 to both sides: x = 4 ±√8

So the solutions are: x = 4 + √8 and x = 4 - √8.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.