Question

How do you solve `5sqrt(a-3)+4=14` and check your solution?

Answer 1

`a = 7`

Explanation:

`5 sqrt(a-3) + 4 =14`

reduce `4` to both sides.
`5 sqrt(a-3) + 4 - 4=14 -4`
`5 sqrt(a-3) =10`

divide `5` to both sides
`(5 sqrt(a-3)) /5 =10/5`
`sqrt(a-3) =2`

square to both sides
`(sqrt(a-3))^2 =2^2`
`a-3 =4`

add `3` to both sides
`a - 3 + 3=4 + 3`
`a = 7`

we check Left hand side to prove right hand side by plug in `a = 4`.
`5 sqrt(7-3) + 4 = 5 sqrt(4) + 4 = 5 * 2 + 4 = 14 ->`proved

Answer 2

`a=7`

Explanation:

`color(blue)"Isolate"` the root on the left side and place numeric values on the right side.

subtract 4 from both sides.

`5sqrt(a-3)cancel(+4)cancel(-4)=14-4`

`rArr5sqrt(a-3)=10`

divide both sides by 5

`(cancel(5)^1sqrt(a-3))/cancel(5)^1=10/5`

`rarrsqrt(a-3)=2larrcolor(red)" root isolated on left side"`

`"to'undo' the root "color(blue)"square both sides"`

`(sqrt(a-3))^2=2^2`

`rArra-3=4`

add 3 to both sides.

`acancel(-3)cancel(+3)=4+3`

`rArra=7`

`color(blue)"As a check"`

Substitute this value into the left side and if equal to the right side then it is the solution.

`5sqrt(7-3)+4=5sqrt4+4=(5xx2)+4=14`

`rArra=7" is the solution"`