Question

Give the solution set to the equation below

Answer 1

\[2x ^{2}-5=x ^{2}+5+4x\]

Answer 2

@Hero

Answer 3

okay first combine the liked terms by getting them to the same side

Answer 4

okay

Answer 5

once you have everything to the same side write it out so i could see it

Answer 6

so x^2-4x=10?

Answer 7

yes but put the ten on the same side as the x's

Answer 8

so x^2-4x-10=0

Answer 9

okay what would be the next step

Answer 10

You have a quadratic function for which you can find the values of x.

Answer 11

could you please expplain how to do it

Answer 12

There are no factors that will satisfy that quadratic function, so you use the method of completing the square in order to find your solutions.

Answer 13

\[x^2-4x-10=0\]Group your x terms together and add +10 to both sides of the equation.

Answer 14

okay a sec

Answer 15

okay i did that
so i get x^2-4x=10

Answer 16

Good.

Now we need to complete the quadratic function on the left hand side of the equation to put it in the form \(ax^2+bx+c\). In order to find c, we use the equation \[c=\left(\frac{b}{2}\right)^2\]Our b = -4.

Can you find the new c value?

Answer 17

would have been easier to use the quadratic equation. -b+ or- the square root of b^2-4ac all over 2a

Answer 18

It works the same way :P

Answer 19

okay, i never used that way.. so i was a little confused

Answer 20

@Ssaharan did you get lost? :o

Answer 21

i got -4 for c

Answer 22

sorry yes i was trying to figure it out using the quadratic formula

Answer 23

actually it is +

Answer 24

oh okay

Answer 25

what would be the next step?

Answer 26

@16shuston

Answer 27

\[c=\left(\frac{-4}{2}\right)^2 = (-2)^2 = +4\] So we complete our quadratic on the left side. Remember, completing the square on the left means we add the same number on the right, its to keep our equation consistent.
\[x^2-4x\color{red}{+4}=10\color{red}{+4}\]Complete the square on the left side and simplify the right. \[(x-2)^2=14\]

Answer 28

so i just solve for x?

Answer 29

Yep.

Answer 30

okay give me a minute

Answer 31

so i got x^2-4x=10

Answer 32

We had that earlier, then we completed the square on the left side of your equation. Did you follow my earlier posts?

Answer 33

yes i did

Answer 34

So in order to find our x-value, we need to square root both sides of our equation. \[\sqrt{(x-2)^2}=\pm \sqrt{14}\]This eliminates the square, and alows us to solve for the linear function. \[x-2=\pm\sqrt{14}\]Can you solve for x now? :)

Answer 35

yes hah give me a minute . thank you for being patient

Answer 36

is it x= 2+sqrt 14 and 2- sqrt 14?

Answer 37

Yep :)

Answer 38

thank you :)

Answer 39

can you please help me in one more question?

Answer 40

Cant atm, kind of have to go :\

Answer 41

Good luck with your other questions though!

Answer 42

its okay thanks!