Question

Can somebody walk this through with me?
If the side length of a square can be represented by 2x + 10 and its area is 256 square units, find the value of x.

Answer 1

The area of a square is the square of the side, right?

Answer 2

Yeah

Answer 3

This square has a side of 2x + 10, so its area is \((2x + 10)^2 \)

Answer 4

2x = 256- 10
2x = 246
x = 123
that easy to do!!

Answer 5

We also know the area is 256 sq units.

Answer 6

It's not 123, that's what I wrote and it was marked incorrect.

Answer 7

Not quite, @ashuu

Answer 8

Since we have an expression for the area and the area itself, we make them equal and solve the equation.

Answer 9

that nt r8 !!

Answer 10

\( (2x + 10 )^2 = 256 \)

Answer 11

@ashuu you saved like four letters typing that

Answer 12

okey i havt seen that mathstudent55

Answer 13

Square the binomial on the left side:
\(4x^2 + 40x + 100 = 256 \)

Answer 14

Now subtract 256 from both sides.

\(4x^2 + 40x - 156 = 0 \)

Answer 15

4x2+40x=156
x2+x=39
The two means squared

Answer 16

We need to factor the left side, but we can divide both sides by 4 since every term is divisible by 4.

\(x^2 + 10x - 39 = 0 \)

Answer 17

Yeah so do you do the square root of 39

Answer 18

Correct?

Answer 19

The final answer is supposed to be x=3. I am still really confused as to how you get to that.

Answer 20

I'm getting there. Just follow along.


Now we can factor the left side:
\( (x - 3)(x + 13) = 0 \)

Set each factor equal to zero:
\( x - 3 = 0\) or \(x + 13 = 0 \)

Solve each equation:
\( x = 3\) or \(x = -13 \)

Answer 21

They both end up equaling zero. Whats the next step?

Answer 22

What are you writing that seriously takes 4 minutes to type?

Answer 23

Now that we have two solutions, x = 3 and x = -13.
We try them in our original problem.

The side of the square is 2x + 10:
For x = 3, 2x + 10 = 2(3) + 10 = 6 + 10 = 16
For x = -13, 2x + 10 = 2(-13) + 10 = -26 + 10 = -16

Now we see that using x = 3, we get a side length of 16 units. A positive number is certainly acceptable as a side length. We keep the answer x = 3.

We also see that using the answer x = -13 gives us a side length of -16 units. A side length cannot be a negative number, so we must disregard the x = -13 solution.

The answer to the problem is:
x = 3

Answer 24

Okay thanks

Answer 25

Let me quote you:
"Can somebody walk this through with me?"

If you want a walk through, you need to be patient.
I could have done all the math with no explanations much faster, but then I'd understand it, but you wouldn't. That wouldn't be very helpful.

Answer 26

You're welcome.

Answer 27

Yeah sorry I got impatient, my Dad is bugging me to go to bed.

Answer 28

listen to your dad. do some more math tomorrow