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How do you solve #x^2 - 4x = -3# by completing the square?

Answer 1

Abigail Allen

#x=3# OR #x=1#

To make the left side of the equation a perfect square, we want to add a number to both sides of the equation:

To do that, we look at #b# (the number next to #x#) and see that it is #-4#

If you add #(b/2)^2# to both sides, the equation on the left will be a perfect square or:

#(-4/2)^2=(-2)^2=4#

So:

#x^2-4xcolor(red)(+4)=-3color(red)(+4)#

#(x-2)^2=1#

#sqrt((x-2)^2)=sqrt(1)#

#x-2=1# OR #x-2=-1#

#x=3# OR #x=1#

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Answer 2

Savannah Anderson

To solve the equation x^2 - 4x = -3 by completing the square, first, move the constant term to the other side to isolate the quadratic terms. This gives you x^2 - 4x + 3 = 0. Next, take half of the coefficient of x, which is -2, square it, giving you 4. Add and subtract this value inside the parentheses. This gives you x^2 - 4x + 4 - 4 + 3 = 0. Now, rewrite the equation as a perfect square trinomial plus a constant. This gives you (x - 2)^2 - 1 = 0. Finally, solve for x by adding 1 to both sides and taking the square root, which gives you x - 2 = ±√1. Thus, x = 2 ± 1. So, the solutions are x = 1 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.