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

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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.
User OJNSim
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