SOLUTION: sqrt-5a+6 = -a (-5a+6 are all under the same square root sign) I'm not asking for someone to give me the answer. I just need help with all the steps, if you would like to give

Question 851512: sqrt-5a+6 = -a
(-5a+6 are all under the same square root sign)
I'm not asking for someone to give me the answer. I just need help with all the steps, if you would like to give the answer, that would still be appreciated, but not a complete necessity. Thanks!
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
sqrt(-5a+6)=-a

Putting triple left braces on the left and triple right braces on the right, renders as this:

Square both sides, simplify, and you can solve for a.

and the left side is factorable.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sqrt(-5a+6) = -a
square both sides to get:
-5a+6 = (-a)^2
since (-a)^2 is equal to a^2, your equation becomes:
-5a+6 = a^2
add 5a and subtract 6 from both sides of this equation to get:
0 = a^2 + 5a - 6
commute this equation to get:
a^2 + 5a - 6 = 0
factor this equation to get:
(a+6) * (a-1) = 0
solve for a to get:
a = -6 or a = 1
now substitute each of these values in your original equation to see if they are good solutions or are extraneous solutions.
when you replace a with -6, your original equation becomes:
sqrt(-5(-6)+6) = 6 which becomes:
sqrt(30+6) = 6 which becomes:
sqrt(36) = 6 which becomes:
6 = 6 which is good, so the a = -6 is a good solution.
when you replace a with 1, your original equation becomes:
sqrt(-5(1)+6) = -1 which becomes:
sqrt(-5+6) = -1 which becomes:
sqrt(1) = -1 which is not a valid solution because sqrt(1) is equal to 1 and not -1.
you can see this graphically by plotting both equations on the same graph and looking for the intersections.
it is at the intersections that both equations have a common solution.
you can see from the graph that there is an intersection when x = -6 but not an intersection when x = 1.

the solution is when x = -6 only.

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