SOLUTION: 1. x^2+6x-5=0 2. 4x^2 + 20x = 0 3. 3x^2 + 10x + 8 = -17x - 2 4. x^2 + 3x - 40 = 0 5. p^2 + 15p + 25 = 6p + 5 6. x^2 = 10x - 24

Algebra ->  Rational-functions -> SOLUTION: 1. x^2+6x-5=0 2. 4x^2 + 20x = 0 3. 3x^2 + 10x + 8 = -17x - 2 4. x^2 + 3x - 40 = 0 5. p^2 + 15p + 25 = 6p + 5 6. x^2 = 10x - 24       Log On


   

Question 118006: 1. x^2+6x-5=0
2. 4x^2 + 20x = 0
3. 3x^2 + 10x + 8 = -17x - 2
4. x^2 + 3x - 40 = 0
5. p^2 + 15p + 25 = 6p + 5
6. x^2 = 10x - 24
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two help you get started

#1

Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2%2B6%2Ax-5=0 ( notice a=1, b=6, and c=-5)




x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A1%2A-5+%29%29%2F%282%2A1%29 Plug in a=1, b=6, and c=-5



x+=+%28-6+%2B-+sqrt%28+36-4%2A1%2A-5+%29%29%2F%282%2A1%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B20+%29%29%2F%282%2A1%29 Multiply -4%2A-5%2A1 to get 20



x+=+%28-6+%2B-+sqrt%28+56+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Asqrt%2814%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-6+%2B-+2%2Asqrt%2814%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-6+%2B+2%2Asqrt%2814%29%29%2F2 or x+=+%28-6+-+2%2Asqrt%2814%29%29%2F2


Now break up the fraction


x=-6%2F2%2B2%2Asqrt%2814%29%2F2 or x=-6%2F2-2%2Asqrt%2814%29%2F2


Simplify


x=-3%2Bsqrt%2814%29 or x=-3-sqrt%2814%29


So these expressions approximate to

x=0.741657386773941 or x=-6.74165738677394


So our solutions are:
x=0.741657386773941 or x=-6.74165738677394

Notice when we graph x%5E2%2B6%2Ax-5, we get:



when we use the root finder feature on a calculator, we find that x=0.741657386773941 and x=-6.74165738677394.So this verifies our answer



#2


4x%5E2%2B20x=0 Start with the given equation

4x%28x%2B5%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
4x=0 or x%2B5=0

x=0 or x=-5 Now solve for x in each case


So our answer is
x=0 or x=-5


Notice if we graph y=4x%5E2%2B20x we can see that the roots are x=0 and x=-5 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+4x%5E2%2B20x%29+