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

2 Answers
salamat
Apr 11, 2017

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

Jim G.
Apr 11, 2017

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"

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