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https://latex.artofproblemsolving.com/miscpdf/ujuyolds.pdf?t=1566795355878 We can find all the solutions of the equation $|x^2-14x+29|=4$ by splitting it up into two cases: $$x^2-14x+29=4$$ $$-x^2+14x-29=4$$ Looking at the first case, where $x^2-14x+29\geq 0$, we begin to notice that in the form of a quadratic $ax^2+bx+c$ $a$ is 1 and $b$ is even, making the scenario the easiest to complete the square. $$x^2-14x+29=4$$ $$x^2-14x=-33$$ $$x^2-14x+49=-33+49$$ $$(x-7)^2=16$$ $$x-7=\pm 4$$ We can then split this into two cases again: $$x-7=+4$$ $$x-7=-4$$ $$x=11$$ $$x=3$$ Now that we found the values of $x$ when $x^2-14x+29\geq 0$, we can move on to our second case of when $x^2-14x+29<0$ $$-x^2+14x-29=4$$ $$-x^2+14x-33=0$$ $$(-x+11)(x-3)=0$$ $$x=11, 3$$ Interesting... Now that we have our final two values of $3, 11$ we have to check these values in case there are many erroneous cases since in the first case we took the square root of both sides.

We can first notice that the expression $4^x-2^x$ contains powers of two, in which we can simplify $4$ into $2^2$ $$4^x - 2^x = 56$$ $$2^{2^x} - 2^x = 56$$ $$2^{2\cdot x} - 2^x = 56$$ $$2^{2x}-2^x=56$$ We can then use our past property about how $x^y\cdot x^z=x^{y+z}$ to separate $2^{2x}$ into $2^2\cdot 2^x$ $$2^{2x}-2^x=56$$ $$2^2\cdot 2^x-2^x=56$$ Letting $2^x$ be $y$ will make things easier to see. $$2^2\cdot y-y=56$$ $$4y-y=56$$ $$3y=56$$ $$y=\frac{56}{3}$$ Plugging $y$ back in gives us: $$2^x=\frac{56}{3}$$ We can separately visualize a graph for both sides of the equal to see how many solutions there are for $x$. $2^x$ would look something like the green line while 56/3 would look something like the blue line. We see that the two graphs meet and will only meet at one point as green will keep on increasing and won't ever come back down. The other side from line green will also only get closer to reaching 0 meaning there is only one point of inter

    Recently I've gone in a low-key cooking phase with tasty and bon appetit videos flooding my recommended on YouTube. There are so many videos like "five easy recipes you can make right now!" The first recipe involves something like expresso powder and you have to boil some stuff man. Anyway what I'm trying to say is that these are actually easy. I've gone through a lot of "testing" basically drinking and adding ingredients and reblending until it just feels right. I've made all of these smoothies enough time to have a perfect proportion so yeah. If you use premade lemon juice then you're a loser jk. We grow lemons so yeah that's easy. Anyway it's equivalent to I'd say 1/9 cup lemon juice? something like that ALL OF THESE RECIPES MAKE ONE SERVING STRAWBERRY LEMONADE RECIPE Servings: 1 Ingredients: 1 cup strawberries with no leaf one medium-sized lemon squeezed(add zest if you want) 1/2 cup milk 8 blocks ice 3/4 tbs

It's Saturday night where I can finally have some time to right after a trip to the park right after a 9-4 marching band practice. Anyway, this week was my first week in high school, and here is what I have to say. The bathrooms are decently clean -I would even say it's cleaner then the Harvest Park bathrooms but either way I expected some really garbage dump in the bathroom but it was decently clean with not too noticeable graffiti.  The bathrooms... -I started on a positive note and now it's time to go down. High school is insane. Many of my friends have stated to smell a fruity strong smell that makes people feel lightheaded in the bathroom, with the main source being a standing person stalling in the stalls of the bathroom with let's just say an illegal thing. Luckily I haven't faced something like that...YET The teachers are actually nice- According to a lot of my high school friends teachers do not teach and are very laid back. I don't know if

Recently I have been drinking this for breakfast for band camp because of its quickness and taste. Servings: 1 Ingredients: 1 cup Reese's puffs 5/8 cup milk 2 medium scoops vanilla ice cream 6 ice blocks(can bring down if you want) OPTIONALS: 2 large scoops ice cream 1 teaspoon honey 1 teaspoon vanilla extract any amount of chocolate chunks or chocolate chips Lowkey unhealthy but it tastes so darn good. Very simple three ingredient recipe(replace ice with water because ice cream is cold itself). As I'm writing this post it is like 10 AM and I'm drinking it for breakfast. Anyway, this is a weird post but I thought that I should share this nice recipe. I will try to post a post about band camp today. I will be experimenting with this recipe, potentially adding banana, berries, or any other type of flavors. Lyric(s) of the Post: It's really hard to see With colors painted on Colorblind – Panda Eyes

Alright so after staying in Rome for two days, we were going to go on a cruise! We went on a cruise ship called celebrity edge, and it WAS HECKA FUN. This video is pretty good but kinda boring lol.  CRUISE SHIP: Free food Free performances you get to watch Awesome service Let's just get right into it. DAY 6      I woke up and had to pay for hotel breakfast which tasted really bad too so it was a lose-lose lol.  We then took a 40 minute taxi to where we would go on the cruise ship, and once we got there we spent almost an hour trynna figure out how to get on the cruise ship. We ended up having to take a bus and stuff. Shout out to skinny bike man with sunglasses for telling us where to go. I saw this on the way. Hi cat And that This wasn't the one we would go on, but as a kid going on a Looney-tunes themed cruise ship is probably your dream.  After a security check....WE IN BOIIISISISISISS I WAS SO EXCITED. Once

My third time going to great america I have no words and am completely truly devastated in a racial mass shooting in Texas. Throughout this past month There has got to be a shooting once a week.  I don't know what to say anymore. Like what my sister said: "If things are still the same since the Parkland shooting and Las Vegas shooting, why will something be changed now?" :| wth man i finish eating breakfast and another holy ok omg aoewkrawrewuoriwauehrwaiereuw wth man wt actual haa oiwehriwaehrwaoeirh uewailruwaeorhiewaourhaoiewhriewaohrweirhawoieuhwaoieruhw ew irwiaerhwar >:( eaoirjeairauhreapieur aeroiuhe ok imma try to write aw fudge man this  ok i need ok lets do this aoirwjeapr Second time First time Alright sigh UGHGHGHGHGHGHG IM SO FUDGING ANNOYED RIGHT NOW WTF IS WRONG WITH THIS AHIUERHAWEORWUAIHROIUAERIAHR ' Okay so basically I went on Friday, August 2nd.