0 like 0 dislike
0 like 0 dislike
[Algebra 1] Need clarification in Quadratic equations

5 Answers

0 like 0 dislike
0 like 0 dislike
First subtract 4 from both sides to get

     -(t - 7)^2 = -4

then multiply both sides by -1.
0 like 0 dislike
0 like 0 dislike
Multiply both sides by (-1) and then add 4.
0 like 0 dislike
0 like 0 dislike
OP, keep it up!

this type of self reflection on your work is what will help you become much better at math.
0 like 0 dislike
0 like 0 dislike
Going forward, these equations should always be solved by taking the square root of both sides.
0 like 0 dislike
0 like 0 dislike
In general, for a equation of the type:

a x \^ 2 + bx + c = 0

there are different ways to solve them depending on whether b and c are 0.  
If b = 0, for example x \^ 2 - 9 = 0, you can just rearange it to: x \^ 2 = 9. Then take the sqrt on both sides to get x = +-3.

Now if c = 0, for example x \^ 2 - 2x = 0, you can always factor out the x and get to: x \* ( x - 2) =0. Now this product is 0 if either x = 0, so this is our first root, or if x - 2 = 0, which gives us the solutions x = 0 and x = 2.

Now the last case is if b and c are non-zero. Note that completing the square is just a way to reformulate everything using the first or second binomial formula.

For example, if we start with x\^2 + 6x + 7 = 0, we try to add some a to both sides, such that we can actually use the binomial formula. In this case, we have x\^2 + 6x. The binomial formula is (x+c)\^2 = x\^2 + 2c x + c\^2. For us the 6x corresponds to 2 c x, which implies that c = 3. So if we add and subtract c\^2 we have:

x\^2 + 6x + 3\^2 - 3 \^2 +  7 = 0,

Now the first three terms are in the correct form to use the binomial formula and we get:  


(x + 3)\^2 - 9 + 7 = 0

(x + 3)\^2 - 2 = 0

And you know how to solve it from here. Note that the equation you linked is already in that form if you multiply it with -1:

(t - 7)\^2 - 4 = 0

So basically, in the example you have provided, somebody has already done the completing the square part, so there's no need for you to do that again.

Related questions

0 like 0 dislike
0 like 0 dislike
0 answers
MorganHoover_ asked Jun 21
"Previous comparison of change in CAPS score between sertraline and placebo showed effect sizes of 0.31 and 0.37 (ref. 16). Similarly, comparison of change in CAPS score ...
MorganHoover_ asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
TylerReddick asked Jun 21
Hello Stats, I am trying to model frequency of an event, and I am looking for the best way to do this. My response variable is frequency, and I am fitting it with Poisson...
TylerReddick asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
_moadams asked Jun 21
I am running a LGCM and have identified a best fitting, two-class trajectory. The problem is that when I open the plots to see the estimated means and observed individual...
_moadams asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
ansaeuropa asked Jun 21
Hi! I thought that this would be a perfect place to discuss about my current project I'm thinking of doing. I have the chance to explore Trackman data, (trackman is a dev...
ansaeuropa asked Jun 21
0 like 0 dislike
0 like 0 dislike
26 answers
PawSox asked Jun 21
I have training in physics and maths and have been looking at statistical programming jobs in the private sector (mostly biotech), and it seems like every single company...
PawSox asked Jun 21
by PawSox

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!