SOLUTION: i need help with these two quadratic equations, please(: 3(x-4)squared=18 and the other one.. 4(x+9)squared=24 if anyone doesnt mind helping me out it would be so awesome!!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: i need help with these two quadratic equations, please(: 3(x-4)squared=18 and the other one.. 4(x+9)squared=24 if anyone doesnt mind helping me out it would be so awesome!!      Log On


   

Question 455619: i need help with these two quadratic equations, please(:
3(x-4)squared=18
and the other one..
4(x+9)squared=24
if anyone doesnt mind helping me out it would be so awesome!!
Thanks!
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
3(x-4)^2=18
(x-4)^2=6

4(x+9)^2=24
divide by 4
(x+9)^2=6

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3%28x-4%29%5E2=18
3%28x-4%29%5E2%2F3=18%2F3
%28x-4%29%5E2=6..
x%5E2-8x%2B16=6..
x%5E2-8x%2B16-6=0
x%5E2-8x%2B10=0......use quadratic formula
Solved by pluggable solver: Quadratic Formula
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%5E2-8%2Ax%2B10=0 ( notice a=1, b=-8, and c=10)





x+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Plug in a=1, b=-8, and c=10




x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Negate -8 to get 8




x+=+%288+%2B-+sqrt%28+64-4%2A1%2A10+%29%29%2F%282%2A1%29 Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because %28-8%29%5E2=-8%2A-8=64.)




x+=+%288+%2B-+sqrt%28+64%2B-40+%29%29%2F%282%2A1%29 Multiply -4%2A10%2A1 to get -40




x+=+%288+%2B-+sqrt%28+24+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%288+%2B-+2%2Asqrt%286%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+=+%288+%2B-+2%2Asqrt%286%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%288+%2B+2%2Asqrt%286%29%29%2F2 or x+=+%288+-+2%2Asqrt%286%29%29%2F2



Now break up the fraction



x=%2B8%2F2%2B2%2Asqrt%286%29%2F2 or x=%2B8%2F2-2%2Asqrt%286%29%2F2



Simplify



x=4%2Bsqrt%286%29 or x=4-sqrt%286%29



So the solutions are:

x=4%2Bsqrt%286%29 or x=4-sqrt%286%29






4%28x%2B9%29%5E2=24

4%28x%2B9%29%5E2%2F4=24%2F4
%28x%2B9%29%5E2=6
x%5E2%2B18x%2B81=6
x%5E2%2B18x%2B81-6=0
x%5E2%2B18x%2B75=0
Solved by pluggable solver: Quadratic Formula
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%2B18%2Ax%2B75=0 ( notice a=1, b=18, and c=75)





x+=+%28-18+%2B-+sqrt%28+%2818%29%5E2-4%2A1%2A75+%29%29%2F%282%2A1%29 Plug in a=1, b=18, and c=75




x+=+%28-18+%2B-+sqrt%28+324-4%2A1%2A75+%29%29%2F%282%2A1%29 Square 18 to get 324




x+=+%28-18+%2B-+sqrt%28+324%2B-300+%29%29%2F%282%2A1%29 Multiply -4%2A75%2A1 to get -300




x+=+%28-18+%2B-+sqrt%28+24+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-18+%2B-+2%2Asqrt%286%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+=+%28-18+%2B-+2%2Asqrt%286%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-18+%2B+2%2Asqrt%286%29%29%2F2 or x+=+%28-18+-+2%2Asqrt%286%29%29%2F2



Now break up the fraction



x=-18%2F2%2B2%2Asqrt%286%29%2F2 or x=-18%2F2-2%2Asqrt%286%29%2F2



Simplify



x=-9%2Bsqrt%286%29 or x=-9-sqrt%286%29



So the solutions are:

x=-9%2Bsqrt%286%29 or x=-9-sqrt%286%29