How to I factorise/solve this equation?

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- nosnip

How to I factorise/solve this equation?

- jamiebookeater

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- nosnip

\[y ^{2} - x - 6x ^{2}\]

- nosnip

= 0

- nosnip

Do you know what type of equation it even is so I can google it?

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## More answers

- UnkleRhaukus

you can rearrange it
\[y^2−x−6x^2 = 0\]
\[0 = 6x^2+x-y^2\]
so it looks like a quadratic,
where \(a= 6\), \(b=1\), \(c=-y^2\)
solve with the quadratic formula

- nosnip

ah okay that's I wasn't sure if it was a quadratic :)

- UnkleRhaukus

(i'm assuming there is no other information give about y)

- nosnip

well it's part of a simultaneous equation? I'm confused because it's a non-calculator question and this seems difficult without a calculator

- nosnip

\[y - 3x + 2 = 0\]
\[y ^{2} - x - 6x ^{2} = 0\]

- UnkleRhaukus

so you have two equations?

- UnkleRhaukus

What do you get if you solve the first one
\[y-3x+2=0\]for \(y\)?

- nosnip

y = 3x + 2

- UnkleRhaukus

substitute this into the second equation
\[y^2−x−6x^2=0\\
\downarrow\\
(3x + 2)^2-x-6x^2 =0\]
This is a quadratic equation in \(x\),
solve for both values of \(x\)

- UnkleRhaukus

(after simplifying)

- nosnip

okay give me a second :)

- nosnip

Do you get the quadratic \[3x ^{2} + 11x + 4 = 0\]

- UnkleRhaukus

almost, but the middle term isn't right

- nosnip

I'm not sure what else it could be?

- UnkleRhaukus

What did you get for the expansion of
\[(3x-2)^2=\]

- nosnip

\[9x ^{2} + 12x +4\]

- UnkleRhaukus

\[(a-b)^2=a^2-2ab+b^2\]

- nosnip

I'm still not seeing where I went wrong sorry!

- UnkleRhaukus

the +12 should be -12

- nosnip

ooh yes sorry you're right okay I can do it myself from there thankyou :)

- nosnip

I've got to go out but thatnlyou for your help I will give it a go later

- UnkleRhaukus

you should now use the quadratic formula
on the right (simplified) quadratic equation
to get two nice values of x,
then back substitute into equation 1, to get the corresponding y's

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