Question

Thirty times the square of a non-zero number is equal to eight times the number. what is the number?

Answer 1

let's say number is x , then

30 × (x)^2 = 8x

subtracting 8x from both side

30x^2 - 8x = 0

taking 2x common

2x( 15x - 4)= 0

one solution is

2x = 0

x= 0

but number is non zero so ignoring it.

next solution is

15x - 4 = 0

adding 4 both side

15x = 4

dividing by 15 both side

x = 4/15

Answer 2

let a non zero number be x

30 times the square root of a non zero number is 30sqrt%28x%29

equal to 8 times the number is 8x

so, we have

30sqrt%28x%29=8x...you can solve for x if you square both sides

%2830sqrt%28x%29%29%5E2=%288x%29%5E2

30%5E2%28x%29=64x%5E2

900x=64x%5E2

64x%5E2-900x=0

x%2864x-900%29=0....use zero product rule

x%2864x-900%29=0 if x=0..this is a solution, but our number should be non zero; so, we need other solution

or if %2864x-900%29=0 => 64x=900=> x=900%2F64=> x=14.0625

so, a non zero number be x=14.0625 and this is your solution

let's check this solution:

30sqrt%28x%29=8x

30sqrt%2814.0625%29=8%2A14.0625

30%283.75%29=112.5

112.5=112.5.....this confirms that our answer is correct .

sorry i messed up there.