How do you solve #(x-1)^2=4#?
Using the quadratic formula, you can find that x=-1 and x=3
On my first reaction, i thought that you could just take the square root of both sides and have your answer... which is 3. However, I remembered at the last minute that the square of a negative number is positive, so that means there are two possible solutions.
Without using the quadratic formula, I guessed that x-1 has to equal 2 or -2, meaning that x could be 3 (3-1=2) or -1 (-1-1=-2).
Since this is a method for solving a quadratic, we'll also use the quadratic formula. First we have to expand the exponential via FOIL:
Now we re-write the equation:
Now we move 4 to the Left-hand Side (LHS) to set up our quadratic:
our coefficients for the quadratic equation are:
plug them into the quadratic equation:
and you solve once for "-b+..." and again for "-b-..."