4/9w^2+1=5/3w  solve by factoring

Asked on by tdt3

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embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

Solve `4/9 w^2+1=5/3 w` :

`4/9 w^2-5/3 w+1=0`  It is easier if you multiply through by 9 to clear the fractions:

`4w^2-15w+9=0` We seek two numbers whose product is 36 and whose sum is -15 -- the numbers are -12 and -3



`(4w-3)(w-3)=0`  Using the zero product property:

`4w-3=0 ==> w=3/4`  and w-3=0 ==> w=3


The two solutions are `w=3/4,w=3`


mufarochamu's profile pic

mufarochamu | (Level 1) eNoter

Posted on

change the improper fractions into whole numbers by multiplying everything by 9.

the function becomes


it now becomes easier to solve. Put everything on one side





therefore w=3 and w=3/4

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