Question

1. Solve: y2 + 7x = 30

2. Solve: x2 + 7 = -8x

3. Solve: x2 – 26x + 48 = 0

4. Solve: x2 - 4x = 32

5. Solve: w(6w + 12) = 0

6. Solve: y2 + y = 30

7. Solve: (a – 5)(a + 3) = 0

Answer 1

That's a lot to solve hehe!

Answer 2

Do you know anything about quadratic equations?

Answer 3

No not really

Answer 4

All right. You're ready to embark on a journey :)

Answer 5

There are infinite number of ways to solve a quadratic equation, but you may use the formula to start.

Answer 6

A quadratic equation looks like:
\(ax^2 + bx + c = 0\)
It has 2 number of solutions(maximum)

Answer 7

ok

Answer 8

And the formula to solve for \(x\) is:

\( \color{Black}{\Rightarrow \Large x = {-b \pm \sqrt{b^2 - 4ac} \over 2a} }\)

Answer 9

right ..

Answer 10

Do you know what \(\pm\) means?

Answer 11

yess

Answer 12

Yes, anyway, it means that x as two solutions:

\( \color{Black}{\Rightarrow \Large {x = {-b + \sqrt{b^2 - 4ac} \over 2a}} }\)

OR

\( \color{Black}{\Rightarrow \Large x = {-b - \sqrt{b^2 - 4ac} \over 2a} }\)

Answer 13

right soo then i just plug in ?

Answer 14

yep.

Answer 15

Thanks

Answer 16

There's another thing here. The zero product rule.

Answer 17

oh whats that ?

Answer 18

Some of them are given like (a - 5)(a + 3) = 0
Zero product rule says that if a * b = 0, then either a = 0 or b = 0

Answer 19

This is because any number multiplied by 0 is 0! :)

Answer 20

So for example \((a - 5)(a + 3) = 0 \)
Either a - 5 is 0 or a + 3 is 0.
We can equate.

Answer 21

\( \color{Black}{\Rightarrow a - 5 = 0 }\)

\( \color{Black}{\Rightarrow a = 5 }\)

OR

\( \color{Black}{\Rightarrow a + 3 = 0 }\)

\( \color{Black}{\Rightarrow a = -3 }\)

Answer 22

Ohh I get it .
that means the problem cant be solved ?

Answer 23

It can be solved.

Answer 24

That's when another method known as factorization comes in, though it may be difficult for me to explain.

Answer 25

Did you get that (a - 5)(a + 3) = 0 example I gave you?

Answer 26

Yes I get it .
(:

Answer 27

Aha! Is there anything left for me to explain?

Answer 28

i think i have the hang of it . (: Thankyou SoMUCH !

Answer 29

You're welcome :)