Solving radical equations???

Question

can someone help me solve this radical equation please???!

sqrt(4a+7) = -sqrt(a+2)

can you show me the steps so that i can understand how its done??...THANKS :)

Answer 1

sqrt(4a+7) = -sqrt(a+2)

4a + 7 = a + 2 --> squre both sides

4a - a = 2 - 7 --> transposing terms

3a = - 5 --> combining like terms

a = -5/3

Answer 2

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Answer 3

Umm, this one has no answer because no matter what for a you plug into sqrt(4a+7), you have to get back a positive number and a positive cant possibly equal a negative number.

you can try to solve this way but the end result will be that you get an "extraneous root", which is a fancy way of saying the answer you obtain wont work

sqrt(4a+7) = -sqrt(a+2)

square both sides

4a+7 = a+2

3a = -5

a= -5/3

but plug in -5/3 into

sqrt(4a+7), sqrt(4(-5/3)+7) = sqrt(1/3)

and into -sqrt(a+2), -sqrt(-5/3 + 2) = -sqrt(1/3)

sqrt(1/3) does not equal -sqrt(1/3)

Answer 4

sqrt(4a+7) = -sqrt(a+2)

square both sides

sqrt(4a+7)^2 = -sqrt(a+2)^2

4a+7 = -(a+2)

4a + 7 = -a - 2

5a = -2 -7

5a = -9

a = - 9/5