How do you solve the equation by completing the square #x^2-14x+33=0#?
The idea of completing the square, otherwise abbreviated as CTS, is not necessarily complex, but it's a bit involved. First, let's remember that a quadratic equation is of the following format:
Now that we've got that out of the way, let's consider the following algebraic term:
Great. But, now what? Well, we add 49 to both sides of the equation! Analyze how I add it in, though.
See what I did there? I injected 49 conveniently, right next to -14x. The question you should be asking is,
Notice how we used the term
Now, let's subtract 33 from both sides.
Now, this is the easy-peezy-lemon-squeazy part. Take the square root of both sides. In doing so, you'll get rid of the exponential 2 on the left side of your equation and on the right side, you'll take the square root of 16. So,
Which further simplifies to
Your solutions are:
Explanation of the
This comes from the proof of the quadratic formula. In fact, one of the ways in which we prove the quadratic formula is through the CTS methodology.