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.
