Question

You must show all your work on each of the following questions.

1. Solve 5x^2 = –45x.

2. Solve x^2 = 14x – 49.

3. Solve x^2 + 18 = –9x.

4. Solve 4x^2 = 12x + 40.

Answer 1

\[5x^2 = –45x\]
\[5 x^2+45 x = 0\]
\[5x(x + 9) = 0\]
\[5x = 0\]
\[x = 0\]
\[(x + 9) = 0\]
\[x = -9\]

Answer 2

For all of these problems, you can rearrange the equations in the form
\[ax^2 + bx + c = 0\]
From there, all you need to do is factorise. The first one, for example, rearranges to 5x^2+45x = 0, which factorises to 5x(x+9)=0. You can see that either 5x=0, or x+9=0, from which you can get two solutions. If you can't factorise the equation, use the quadratic formula.

Answer 3

\[x^2 = 14x – 49\]
\[x^2-14 x+49 = 0\]
\[(x - 7) (x - 7) = 0\]
\[(x - 7) = 0\]
\[x = 7\]
\[(x - 7) = 0\]
\[x = 7\]

so x = 7

Answer 4

\[x^2 + 18 = –9x\]
\[x^2+9 x+18 = 0\]
\[(x+3) (x+6) = 0\]
\[x = -6\]
\[x = -3\]

Answer 5

do you get the hang of it now? @touseii45

Answer 6

@some_someone A bit

Answer 7

hmm well what @Fruitbasket wrote is a good explanation, might want to read it :)

Answer 8

@some_someone why does the answer become the opposite of what came out? like in the last one you put (x+3) (x+6) = 0 but got -3 and -6 rather than 3 and 6. Why is that?

Answer 9

ohh alright. now that makes sense.
i tried doing the last one but i cant seem to factor it right. Like i cant find the right ones for it. @some_someone

Answer 10

\[4x^2 = 12x + 40\]
\[4 x^2-12 x-40 = 0\]
use the quadratic formula.

Answer 11

\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

Answer 12

and in your case it would be like this:
\[ax^2 + bx + c = 0\]
\[4x^2 - 12x - 40 = 0\]
where:
a = 4
b = -12
c = -40

Answer 13

\[x = \frac{ -12 \pm \sqrt{-12^2 - 4(4)(-40)} }{ 2(4) } \]

Answer 14

so its something like this?? @some_someone

Answer 15

\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]
\[x = \frac{ -(-12) \pm \sqrt{(-12)^2 - 4(4)(-40)} }{ 2(4) }\]

Answer 16

your is close but not correct @touseii45

Answer 17

so after all the math x = 5 right? @some_someone

Answer 18

that is only one solution, the equation has to solutions.

Answer 19

did you seperate them into two, since its \[\pm \]

Answer 20

so x = 5 and x = -2 ? @some_someone

Answer 21

precisely :)
good job :D

Answer 22

Thank you so much!! @some_someone

Answer 23

yw :)