Radicals, factoring, quadratics! HELP! I seriously dont get this at all and it's due in the morning! PLEASE?

Question

First of all one of the equations is x squared - 81= 0 and it says 'solve using the square root method' which i dont know how to do.

the second one says 'factor completly' and the question is 8x squared -50

the third one says use the quadratic formula to solve the equation and the question is xsquared -12x - 18 = 0

PLEASE SHOW ME HOW TO DO THIS!

Answer 1

x^2-81=0
x^2=81
x=sq.rt 81=+/-9

2.8x^2-50=2(4x^2-25)=4[(2x)^2-(5)^2]
=2(2x+5)(2x-5)

3.x^2-12x-18=0
x=[12+/-(144+72)^1/2]/2
=[12+/-(216)^1/2]/2
=12+/-6rt6 /2
=6+/-3rt6

Answer 2

x^2 - 81 = 0

By the square root method, move the 81 to the right side and get

s^2 = 81

Then take the square root of both sides:

x = sqrt(81), x = +/-9

By factoring:

81=9^2, so the equation is the difference between perfect squares in the form (a^2-b^2). This expression can always be factored into sum and difference terms (a+b)*(a-b). So in your problem

(x+9)*(x-9) = 0

to make this zero, either factor can be zero, so x=9 or x=-9

Finally, the quadratic formula is a general method for solving any quadratic equation which is in the form ax^2 + bx + c = 0. By comparing, you see that for your problem a = 1, b = 0 c = -81. The quadratic formula is

x = (-b +/-sqrt(b^2 - 4*a*c))/2*a

Plugging the numbers for a, b, c you get

x =( 0 +/-sqrt(0 + 4*81)/2 = +/-sqrt(4*81)/2 = +/-sqrt(324)/2 = +/-18/2 = +/-9

Answer 3

x^2-81=0
=> x^2=81
=> x=squareroot(81)
=> x=+81 or x=-81
both of these are ur answers

8x^2-50
=> 2*(4x^2-25)
=>2*(2x-5)*(2x+5) {since (a^2-b^2=(a+b)*(a-b)}
this is the answer

x^2-12x-18=0

solving this using the quadratic formula, one soultion will be

x= (-b+sqrt(b^2-4*a*c)/(2*a)
the other solution would be
x= (-b-sqrt(b^2-4*a*c)/(2*a)

where b=-12
a=1
c=-18
therfore
x= (12+sqrt( -12^2-4*1*(-18)))/(2*1)
x=((12+sqrt(144+72))/2)
x=(12+14.69)/2
x=13.34

the other root will be
x= (12-sqrt( -12^2-4*1*(-18)))/(2*1)
x=(12-14.69)/2
x=-1.345

These are the two roots of the quadratic equation