Please Help!

[PuppyGirl]

I've been out of school sick for five days. I'm just about caught up with my homework. I just have tihs and another subject to do.

Directions: Find all real-number solutions. I've been factoring the equations to solve them, but on these I'm really stuck. I even asked my dad if he could help me, but he helped me as much as he could. We were just plugging in numbers to see if they worked, that was how I found these awnsers.


x^2+8x+16=0
Hint: an awnser is -4

2x^2-x=3
2x^2-x-3=0
Hint: a couple of the awnsers are 3/2, -1

How do I find the awnsers?(show work)

 

[steve_b]

find all real-number solutions

x[squared]+3x=10
x[squared]+3x-10=0

How do I find the awnser?(show work)

A hint: the awnser is -5

=================

To solve

x^2 + 3x - 10 = 0

you either have to factor it (if possible) or use the quadratic formula. This happens to factor:

x^2 + 3x - 10 = (x +5)(x - 2) = 0

Here you have two quantities being multiplied together and gettiing 0 as a result. The only way for this to happen is for one of the quantities to be equal to 0. So we write:

x + 5 = 0, OR, x - 2 = 0

solving each of these we get:

x = -5 OR x = 2

Those values of x will make the original equation into a true statement

x^2 + 3x = 10

Substitute -5 for x and you can see that this makes a true statement:

(-5)^2 + 3(-5) = 10

25 - 15 = 10

10 = 10 [true]

Likewise for x = 2. [check it]

Hope that helps...

Steve