# Consider this multivariable function. f(x,y)=xy+2x+y−36a) What is the value of f(2,−3)?b) Find all x-values such that f (x,x) = 0

Consider this multivariable function. $f\left(x,y\right)=xy+2x+y-36$
a) What is the value of $f\left(2,-3\right)$?
b) Find all x-values such that $f\left(x,x\right)=0$

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a) We find $f\left(2,-3\right)$ be replacing x by 2 and by -3 in $f\left(x,y\right)$
$f\left(2,-3\right)=2\left(-3\right)+2\left(2\right)+\left(-3\right)-36$
$f\left(2,-3\right)=-6+4-3-36=-41$
b) Now, we solve $f\left(x,x\right)=0$ as follow.
$f\left(x,x\right)=0$
${x}^{2}+2x+x-36=0$
${x}^{2}+3x-36=0$
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}=\left(-3±\sqrt{{3}^{2}-4\left(1\right)\left(-36\right)}\right)\frac{\right)}{2\left(1\right)}=\frac{-3±\sqrt{153}}{2}$