Question 136063
a=Square root of 7a-6

I guess you are trying to solve for a , right?

Square both sides:

(a)^2 = (sqrt{7a - 6})^2

a^2 = 7a - 6

Bring the right side to the left side and equate to zero.

a^2 - 7a + 6 = 0

Factor left side.

(a - 6)(a - 1) = 0

Set each factor to zero and solve for a.

a - 6 = 0

a = 6

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a - 1 = 0

a = 1

Final answer: a = 1 and a = 6

We have to check the answers for a because we are dealing with square roots.

CHECKING:

a = sqrt{7a - 6}

I will plug 1 for a and simplify and then plug 6 for a and simplify.  I must get the same answer on BOTH sides of the equation.

Let a = 1

1 = sqrt{7(1) - 6}

1 = sqrt{7 - 6}

1 = sqrt{1}

1 = 1...IT CHECKS!

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Now, let a = 6 and do the same thing again.

6 = sqrt{7(6) - 6}

6 = sqrt{42 - 6}

6 = sqrt{36}

6 = 6...IT CHECKS!

So, now I know for sure that a = 1 and a = 6.

Is this clear?