Question

Find value of x in the rhombus.

Answer 1

I am assuming that the two polynomials you put up there are referring to the two opposite angles.

As in a rhombus the opposite angles are the same, we can just set them equal to each other.\[3x^{2} - 28= 2x^{2} - 3x \]
Moving all the terms to one side we get:
\[x^{2} + 3x - 28= 0 \]
Which can be simplified down to
\[(x-4)(x+7)=0\]
So x = 4 or -7.
However, an angle cannot be negative here, so only the x=4 is a valid answer.

Answer 2

but 4 was negative, why did you change it to positive?

Answer 3

Oh we are looking for a value of x that satisfies the equation
(x−4)(x+7)=0

Therefore, either x-4 or x+7 must be equal to 0.
And that means that x=4 or x=-7.

Answer 4

thank you!!

Answer 5

No problem!

Answer 6

thank you!!