Help me with this two I don't understand

Step-by-step explanation:

5.

Simplify both radicals.

Apply Quadratic Formula

First. find the discramnint.

Now find the divisor 2a.

Then,take the square root of the discrimant.

Finally, add -b.

So our possible root is

Which simplified gives us

Rationalize the denominator.

Which simplified gives us

.

6. The answer is 2.

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  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

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Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2