Question

How do I solve for x^2=40?

Answer 1

\[\Large x^2=40\]If we take the square root of each side we get,\[\Large \sqrt{x^2}=\sqrt{40}\]
The square root and square are inverse operations of one another, so they'll undo one another, or cancel out, whatever makes more sense to you.

We just need to be careful because we're taking the root of a square, we need to account for negative values of x.

Answer 2

\[\Large \pm x=\sqrt{40}\]

Answer 3

We can move the +/- to the other side.\[\Large x=\pm \sqrt{40}\]

Answer 4

To simplify the expression, we need to ask ourselves, does 40 contain any factors that are perfect squares?

The perfects squares are numbers like: 4, 9, 16, 25.
Those are numbers we can easily take a square root of.

Answer 5

Is 40 divisible by any of those numbers? :o

Answer 6

Yea 4

Answer 7

Good good good.
So we can write it like this,\[\Large x=\pm \sqrt{4\cdot10}\]Square root of 4 is? :D

Answer 8

It is 2root10

Answer 9

yay good job \c:/

Don't forget the +/-

Answer 10

Okay thanks! but for example how would I be able to do a harder one like x2-4x=21?

Answer 11

This problem is quite a bit different.
We need to get it into this form first:\[\Large ax^2+bx+c=0\]And then we'll try to see if it factors, if it doesn't we'll resort to using the `Quadratic Formula`.

Answer 12

We'll start by subtracting 21 from each side,\[\Large x^2-4x=21\qquad\to\qquad x^2-4x-21=0\]

Answer 13

We need to find 2 values that will `multiply` to -21,
but also `add` to -4.

\[\Large -21\cdot1=-21, \qquad\qquad -21+1\ne-4\]Hmm those factors won't work...

Answer 14

Let's try these instead:\[\Large -7\cdot3=-21, \qquad\qquad -7+3=-4\]Ah hah! those will work.

Answer 15

\[\Large x^2-4x-21=0\qquad\qquad\to\qquad\qquad x^2-4x+(-7\cdot3)=0\]

Answer 16

So we can factor the expression into a pair of binomials,\[\Large (x+(-7))(x+3)=0\]Which we can write as,\[\Large (x-7)(x+3)=0\]

Answer 17

Factoring is a little hard to explain :[
I hope that makes at least a little bit of sense.

Answer 18

From there, by the `Zero Factor Property`, we can set each individual factor equal to zero and solve for x in each case.\[\Large (x-7)=0 \qquad\qquad\qquad (x+3)=0\]

Answer 19

Okay the answers will be x=7 and x=-3?

Answer 20

Yay good job \c:/