SOLUTION: what is the answer step by step to the following quadratic equations ? x squared-4x-15=0 x squared+8x-33=0 x squared+5x+2=0 3xsquared-3x+6=0 Help would be great i need it bad

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: what is the answer step by step to the following quadratic equations ? x squared-4x-15=0 x squared+8x-33=0 x squared+5x+2=0 3xsquared-3x+6=0 Help would be great i need it bad      Log On


   

Question 120708: what is the answer step by step to the following quadratic equations ?
x squared-4x-15=0
x squared+8x-33=0
x squared+5x+2=0
3xsquared-3x+6=0
Help would be great i need it bad
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to 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%5E2-4%2Ax-15=0 ( notice a=1, b=-4, and c=-15)




x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-15+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=-15



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-15+%29%29%2F%282%2A1%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-15+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)



x+=+%284+%2B-+sqrt%28+16%2B60+%29%29%2F%282%2A1%29 Multiply -4%2A-15%2A1 to get 60



x+=+%284+%2B-+sqrt%28+76+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+2%2Asqrt%2819%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+=+%284+%2B-+2%2Asqrt%2819%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%284+%2B+2%2Asqrt%2819%29%29%2F2 or x+=+%284+-+2%2Asqrt%2819%29%29%2F2


Now break up the fraction


x=%2B4%2F2%2B2%2Asqrt%2819%29%2F2 or x=%2B4%2F2-2%2Asqrt%2819%29%2F2


Simplify


x=2%2Bsqrt%2819%29 or x=2-sqrt%2819%29


So these expressions approximate to

x=6.35889894354067 or x=-2.35889894354067


So our solutions are:
x=6.35889894354067 or x=-2.35889894354067

Notice when we graph x%5E2-4%2Ax-15, we get:



when we use the root finder feature on a calculator, we find that x=6.35889894354067 and x=-2.35889894354067.So this verifies our answer





#2
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%2B8%2Ax-33=0 ( notice a=1, b=8, and c=-33)




x+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A1%2A-33+%29%29%2F%282%2A1%29 Plug in a=1, b=8, and c=-33



x+=+%28-8+%2B-+sqrt%28+64-4%2A1%2A-33+%29%29%2F%282%2A1%29 Square 8 to get 64



x+=+%28-8+%2B-+sqrt%28+64%2B132+%29%29%2F%282%2A1%29 Multiply -4%2A-33%2A1 to get 132



x+=+%28-8+%2B-+sqrt%28+196+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-8+%2B-+14%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-8+%2B-+14%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-8+%2B+14%29%2F2 or x+=+%28-8+-+14%29%2F2

Lets look at the first part:

x=%28-8+%2B+14%29%2F2

x=6%2F2 Add the terms in the numerator
x=3 Divide

So one answer is
x=3



Now lets look at the second part:

x=%28-8+-+14%29%2F2

x=-22%2F2 Subtract the terms in the numerator
x=-11 Divide

So another answer is
x=-11

So our solutions are:
x=3 or x=-11

Notice when we graph x%5E2%2B8%2Ax-33, we get:

+graph%28+500%2C+500%2C+-21%2C+13%2C+-21%2C+13%2C1%2Ax%5E2%2B8%2Ax%2B-33%29+

and we can see that the roots are x=3 and x=-11. This verifies our answer