Question

How do you solve `2y ^ { 2} = 13y - 15`?

Answer 1

`y=5 or y=3/2`

Explanation:

Make 0 the subject, so shift everything to one side of the inequality

`2y^2-13y+15`

find two numbers that multiply to give `2*15` and add up to give `-13`.

Those two numbers are `-3` and `-10`.

Write the equation in which `-13` is a sum of `-3` and `-10`.

`2y^2-3y-10y+15`

Factorise

`y(2y-3)-5(2y-3)`

Factorise further

`(y-5)(2y-3)`

Answer 2

`y=3/2" or "y=5`

Explanation:

`"rearrange into "color(blue)"standard form"`

`rArr2y^2-13y+15=0larrcolor(blue)"in standard form"`

`"using the a-c method of factorising"`

`"the factors of + 30 which sum to - 13 are - 10 and - 3"`

`rArr2y^2-10y-3y+15=0`

`rArrcolor(red)(2y)(y-5)color(red)(-3)(y-5)=0`

`rArr(y-5)(color(red)(2y-3))=0`

`"equate each factor to zero and solve for y"`

`y-5=0rArry=5`

`2y-3=0rArry=3/2`