How do you solve (8x)^(1/2)+6=0?

2 Answers
Jul 27, 2016

x=9/2

x=4.5

Explanation:

(8x)^(1/2)+6=0

Get rid of 6 from left side
For that subtract 6 on both sides

(8x)^(1/2)=-6

Squaring on both sides

8x=36

x=36/8

x=9/2

x=4.5

Jul 28, 2016

There are no values of x which satisfy this equation.

Explanation:

(8x)^(1/2)+6=0

Subtract 6 from both sides to get:

(8x)^(1/2) = -6

Square both sides, noting that squaring may introduce spurious solutions:

8x = 36

Divide both sides by 8 to get:

x = 36/8 = 9/2

Check:

(8x)^(1/2)+6 = (8*9/2)^(1/2)+6 = 36^(1/2)+6 = 6+6 = 12

So this x is not a solution of the original equation.

The problem is that while 36 has two square roots (viz +-6), 36^(1/2) = sqrt(36) = 6 denotes the principal, positive square root.

So the original equation has no solutions (Real or Complex).