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How do you solve #(x-5)^2=4#?

Answer 1

#x in {3, 7}#

#(x-5)^2=4# #rArr# #color(white)("XXX"){: ("either",(x-5)=2,color(white)("XX")"or"color(white)("XX"),(x-5)=-2), (,rarr x=7,,rarrx=3) :}#

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Answer 2

Genesis Allen

To solve the equation (x - 5)^2 = 4, you can follow these steps:

Expand the left side of the equation: (x - 5)^2 = (x - 5)(x - 5) = x^2 - 10x + 25.
Set the expanded expression equal to 4: x^2 - 10x + 25 = 4.
Rearrange the equation to set it equal to zero: x^2 - 10x + 21 = 0.
Factor the quadratic equation: (x - 7)(x - 3) = 0.
Use the zero-product property to find the solutions: Set each factor equal to zero and solve for x:
- Set x - 7 = 0: x = 7.
- Set x - 3 = 0: x = 3.

Therefore, the solutions to the equation (x - 5)^2 = 4 are x = 7 and x = 3.

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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.