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Geometry equation: x squared + 3x = 8x + 6
- Thread starter alee
- Start date
Hello, alee!
Let get this in the form \(\displaystyle \,ax^2\,+\,bx\,+c\,=0\,\) to solve the quadratic:
\(\displaystyle \L \;x^2\,-\,5x\,-\,6\,=\,0\)
Where are you stuck? What have you tried?
\(\displaystyle \L \;x^2\,+\,3x\,=\,8x\,+6\)
Let get this in the form \(\displaystyle \,ax^2\,+\,bx\,+c\,=0\,\) to solve the quadratic:
\(\displaystyle \L \;x^2\,-\,5x\,-\,6\,=\,0\)
Where are you stuck? What have you tried?
alee said:stuck on what to do with the xsquared. I know x squared -5x = 6
Well why didn't you say so? :wink:
Let use the simple 'ole factoring method for this. What 2 number multiply to give you \(\displaystyle - 6\) and add up to \(\displaystyle - 5\) ? Those are \(\displaystyle - 6\,&\,1\).
So now we have:\(\displaystyle \L \;(x\,+\,1)\,\,(x\,-\,6)\,=\,0\)
Which is saying solve these two equations:
\(\displaystyle \L \;x\,+\,1\,=\,0\)
\(\displaystyle \L \;x\,-\,6\,=\,0\)
Those will be your two roots of \(\displaystyle x\).
alee said:or, xsquared - 5x - 6 = 0
x squared - 5x - 6 = (x+6)(x-1) = 0
therefore x = -6 and 1
A positive 6.