Please help very confused

[LCW]

Well i am so confused i have asked my dad for help but he could nto show me i looked all over the web and i have submitted answers i thought were right online numerous times and keep getting them wrong could some kind person just do these 3 simple problems for me ans show work so i can see what i was doing wrong i have like a page for each problem of me repeatedly trying them but i know i am just missing 1 small step. the ^ means to the power of like ^2 to the power of 2 just like on a calculator

1.)The quadratic equation

X^2-2X-1=0
has two real solutions. The smaller one is ?


2.)
1 pt) Solve the equation x^2-6x+8=0

The solutions are X^1= _____ and X^2____

3.)Find all real solutions of the equation x^2-125=0

x^1=____ and x^2=11.18.03 ( i figured that one out)



if you could help that would be really really awesome cuz these are bothering me

 

[chrisr]

Sometimes it's easy to write a quadratic using factors and sometimes it's too difficult.

x[sup:25jc96ij]2[/sup:25jc96ij]-2x-1 is a case where you must use the alternative, the quadratic formula.
ax[sup:25jc96ij]2[/sup:25jc96ij]+bx+c=0 for x= {-b+sqrt(b[sup:25jc96ij]2[/sup:25jc96ij]-4ac)}/2a and x = {-b-sqrt(b[sup:25jc96ij]2[/sup:25jc96ij]-4ac)}/2a.

The smaller one will be the one with the - after -b.

You can do the same with the 2nd one, but that one is easy to write factors for.
Two numbers multiply to give 8 and add to give -6.
They are -4 and -2,

so x[sup:25jc96ij]2[/sup:25jc96ij]-6x+8 = (x-4)(x-2).

If this is zero, what could x be ? since zero multiplied by anything is zero.
The two values of x that cause that to be zero are x[sub:25jc96ij]1[/sub:25jc96ij] and x[sub:25jc96ij]2[/sub:25jc96ij].

For the 3rd, you can rewrite that as x[sup:25jc96ij]2[/sup:25jc96ij] = 125.
Now 3(3) = 9, but -3(-3) is also 9, so what is the value of x[sub:25jc96ij]1[/sub:25jc96ij]?