Quadratic Formula questions...?

Question

Using the quadratic formula to solve these questions:

1. x^2 + 12x + 11 =0

2. -x^2 + 7x - 10 =0

3. 5x^2 + 12 = -6x

solutions and work shown are greatly appreciated.i've been struggling w/this for nearly 2 hrs...

Answer 1

quadratic formula =

-b +/- square root of b^2-4ac divided by 2a
where a is the coefficent of x^2, b is x and c is the constant

for 1

-12 +/- square root 12^2-4(1)(11) divded by 2(1)
= -12 +/- 10 / 2
so root for #1 is -1 and -11

#2 -7 +/- square root of 7^2 - 4(-1)(-10) / 2(-1)
= -7+/- 3 / 2
so roots are -5 and -2

#3 6+/- sqaure root 6^2 - 4(5)(12) / 2(5)
6 +/- square root -204 / 10
answer would be imaginary

Answer 2

Solution:

1. Just by trial and error you know that 11= 11*1 and that 11+ 1= 12

so (x+1)(x+11) = x^2 + 12x + 11

2. Multiplying the equation by -1 you will get,
x^2 - 7x + 10 = 0

you know that 10 = 5*2 and that 5+2 = 7

so,

(x-2)(x-5) = x^2 - 7x + 10 = 0

3. This problem is a little more involved,

5x^2 +6x + 12 = 0

First strategy is completing the square...

divide by 5

x^2 + 6/5x + 12/5 = 0

working with the middle term (x term), 6/5x = 2(3/5)x

completing the square we get

(x+3/5)(x+3/5) = x^2 + 6/5x + 9/25

so
(x+3/5)(x+3/5) + 12/5 - 9/25 = 0

(x+3/5)(x+3/5) + 144/25 - 9/25 = 0
(x+3/5)^2 + 135/25 = 0

the solution involves an imaginary component.

Good luck.

Answer 3

Formula: (-b(+ or -) square root (b^2+4ac))/2a,

where ax^2+bx+c = 0

For the first problem, a=1, b=12 and c=11, so
x=(-12+square root(144+4*1*11))/2*1 as well as
(-12-square root(144+4*1*11))/2*1
so x=0.86 and 12.86

For the second problem, so the same thing, except a= -1, b=7 and c= -10

For the third problem, you need to get everything on the same side of the equation, so:
5x^2+6x+12=0, and a=5, b=6 while c=12.

Does that help?

Answer 4

You have the quadratic equation, right? Check and make sure you have the equation written correctly.

For the first equation, a=1, b=12 and c=11. Just plug those values into the quadratic equation and you'll get two answers. THey should be x=11 and x=1.

For your second equation, a=-1, b=7 and c=-10.

For the third one, you should rearrange it so that all terms are on the left. Then, a=5, b=6 and c=12.

I can't really show you my work here because writing the square root sign is impossible to do.

Good luck....

Answer 5

We all struggled with that... now you have to too...

Good luck!