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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