How do you solve #x^2-8x+5=0#?
We use a process called completing the square, which works for all quadratic equations. Here it gives
Rather than memorizing a formula, you should understand how "completing the square" works.
Render the equation as:
Then add a constant, which we will call
Now compare the left side with the identity
We then have
So,go back to the equation in blue and put in
The standard form of a quadratic is
So, we have
Solutions are given by
Using scientific calculator, we get,
Now, we can write [ Intermediate Result 1 ] as
We can rewrite the above as
Hence, we have the following two solutions:
Using a scientific calculator, we can simplify the above results.
You can verify the solutions visually by examining the image of the graph below:
Hope it helps.