How do you solve for x^2-8x+14=0

I'm going to solve by completing the square because there are no factors of 14 that when added together become - 8. To do so, the first step is to subtract 14 from both sides leaving only the first two terms on the left side of the equal sign:

x² - 8x = - 14

Now, we divide the middle term by 2 and square the quotient. Then add the result to both sides.

- 8 / 2 = - 4, ( - 4) ² = 16.

x² - 8x + 16 = - 14 + 16

x² - 8x + 16 = 2

Now we can factor the left side:

(x - 4) ² = 2

Square root both sides to get rid of the exponent on the left side.

√ (x - 4) ² = √2

x - 4 = + / - √2

Add 4 to both sides to isolate the variable:

x = 4 + / - √2

Your exact answers are:

x = 4 - √2 and x = 4 + √2

You can plug both of those into a calculator if you want approximations.