Solve the equation. If necessary, round your answer to the nearest tenth.

9x2 = 49

2.3, –2.3
5.4, –5.4
7, –7
21, –21

Question

Solve the equation. If necessary, round your answer to the nearest tenth.

9x2 = 49

2.3, –2.3
       5.4, –5.4
       7, –7
       21, –21

juliebeans · Answer

@sammixboo

mathstudent55 · Answer

First, subtract 49 from both sides.
What do you get?

juliebeans · Answer

erhm 1,5.4

mathstudent55 · Answer

$9x^2 = 49$

Start by subtracting 49 from both sides:

$9x^2 - 49 = 0$

juliebeans · Answer

ok

mathstudent55 · Answer

Now factor the left side.
The left side is a difference of squares.
Do you know how to factor a difference of squares?
It follows this pattern:
$a^2 - b^2 = (a + b)(a - b) $

mathstudent55 · Answer

You have $9x^2 - 49$
$9x^2$ is the square of 3x.
49 is the square of 7.
You can rewrite $9x^2 - 49$ as $(3x)^2 - 7^2$ which clearly shows the two squares.

mathstudent55 · Answer

Now you factor the left side using the pattern I showed above.

juliebeans · Answer

Can  we combine the 9x2 and 3x(2) togther?

juliebeans · Answer

@mathstudent55

mathstudent55 · Answer

No.
I'll show you with a drawing to make it easier to see how a difference of squares factors.

juliebeans · Answer

ok

mathstudent55 · Answer

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