SOLUTION: 3d-7 - 3d-2 _____ _____ 2d - 3d squared

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3d-7 - 3d-2 _____ _____ 2d - 3d squared      Log On


   

Question 29636: 3d-7 - 3d-2
_____ _____
2d - 3d squared
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
I am reading this problem as ....
+%283d-7%29%2F%282d%29+=+%283d-2%29%2F%283d%5E2%29+
cross multiply
+%283d%5E2%29%283d-7%29+=+%282d%29%283d-2%29+
distribute
+9d%5E3+-+21d%5E2+=+6d%5E2+-+4d+
move everything to the left
+9d%5E3+-+21d%5E2+-+6d%5E2+%2B+4d+=+0+
combine like terms
+9d%5E3+-+27d%5E2+%2B+4d+=+0+
since the power is cubed, there will be 3 solutions.
for the first, factor out a d
+d%289d%5E2+-+27d+%2B+4%29+=+0+
the first solution is d=0
the trinomial can not be factored. Use the quadratic formula to solve.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 9
b = -27
c = 4
substitute these numbers into the equation
x+=+%28-%28-27%29+%2B-+sqrt%28+%28-27%29%5E2-4%2A9%2A4+%29%29%2F%282%2A9%29+
simplify
x+=+%2827%29+%2B-+sqrt%28+%28+729-144+%29%29%2F%2818%29+
simplify again
x+=+%2827%29+%2B-+sqrt%28+%28+585+%29%29%2F%2818%29+
root out 585
585 = 3*3*5*13
+sqrt%28+585%29+=+3%2Asqrt%2865%29+
the + and - make for the 2 other solutions.
x+=+%2827+%2B-+3%2Asqrt%2865%29%29%2F%2818%29+
reduce all cofficients by dividing each by 3
x+=+%289+%2B-+1%2Asqrt%2865%29%29%2F%286%29+
Those are your 3 answers