Solve each equation by completing the square. If necessary, round to the nearest hundredth.

Question

anonymous · Answer

33. x^2+10x=-8
35. x^2-14x+16=0

anonymous · Answer

Solve each equation using any method. Explain why you chose the method you used.
45. x^2-6x+9=0

mathmale · Answer

First:  be certain that you understand what "completing the square" entails.  You start with a quadratic expression or equation and re-write it in different form, so that the new form contains the square of a binomial.

If, as in #33, you have the quadratic equation $$x ^{2} + 10x=-8,$$ your first goal is to rewrite $$x ^{2}+10x$$

in the form $$(x+5)^{2}=25-8.$$
How?  See the coefficient of the x term in the original equation?  It's 10.  Take half of this coefficient, that is, take half of 10, and square the result.

mathmale · Answer

Add that result to both sides of the original equation.  You'll get:
$$x ^{2}+10x+25-25=-8.$$
Now the first three terms can be re-written as $$\left( x+5 \right)^{2}.$$
Then we'll end up with $$\left( x+5 \right)^{2}$$-25=-8.

anonymous · Answer

Ok thank you.

mathmale · Answer

So...all set, as is?

anonymous · Answer

Huh?

mathmale · Answer

I'd typed a lot more, but lost it.  I wanted to know whether you're now able to finish solving the problem yourself.

anonymous · Answer

Yes.

mathmale · Answer

Great.  just out of curiosity, where are you located?  I'm in Southern California.

anonymous · Answer

South Carolina

mathmale · Answer

Cool.  Good luck!  See you.