#2sqrt (6a + 7) - 2a = 0? #solve the equation

1 Answer
Apr 18, 2017

Answer:

#a = 7#

Explanation:

Given: #2sqrt (6a + 7) - 2a = 0#

Restrict the domain so that the expression under the radical never becomes negative:

#2sqrt (6a + 7) - 2a = 0; a>=-7/6#

Divide the equation by 2:

#sqrt (6a + 7) - a = 0; a>=-7/6#

Add "a" to both sides:

#sqrt (6a + 7) = a; a>=-7/6#

Square both sides:

#6a + 7 = a^2; a>=-7/6#

Subtract #6a+7# from both sides:

#0 = a^2-6a - 7; a>=-7/6#

Factor:

#(a-7)(a+1)=0#

#a = 7 and a = -1#

Please notice that I have can discarded the restriction because neither root violates it.

Check:

#2sqrt (6(7) + 7) - 2(7) = 0#
#2sqrt (6(-1) + 7) - 2(-1) = 0#

#0 = 0#
#2 = 0#

The negative root must be discarded; it is an erroneous root introduced by squaring.

#a=7# is the only correct answer.