Solve y=-x^2-ax^2-1.3x+8x-2

$$y = - x ^ { 2 } - a x ^ { 2 } - 1.3 x + 8 x - 2$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{-10x^{2}+67x-10y-20}{10x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=-2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -1.3x and 8x to get 6.7x.

$$y=-x^{2}-ax^{2}+6.7x-2$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}-ax^{2}+6.7x-2=y$$

Subtract 6.7x from both sides.

$$-x^{2}-ax^{2}-2=y-6.7x$$

Add 2 to both sides.

$$-x^{2}-ax^{2}=y-6.7x+2$$

Add x^{2} to both sides.

$$-ax^{2}=y-6.7x+2+x^{2}$$

The equation is in standard form.

$$\left(-x^{2}\right)a=x^{2}-\frac{67x}{10}+y+2$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{x^{2}-\frac{67x}{10}+y+2}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$a=\frac{x^{2}-\frac{67x}{10}+y+2}{-x^{2}}$$

Divide y+x^{2}-\frac{67x}{10}+2 by -x^{2}.

$$a=-1+\frac{\frac{67x}{10}-y-2}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-10x^{2}+67x-10y-20}{10x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=-2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -1.3x and 8x to get 6.7x.

$$y=-x^{2}-ax^{2}+6.7x-2$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}-ax^{2}+6.7x-2=y$$

Subtract 6.7x from both sides.

$$-x^{2}-ax^{2}-2=y-6.7x$$

Add 2 to both sides.

$$-x^{2}-ax^{2}=y-6.7x+2$$

Add x^{2} to both sides.

$$-ax^{2}=y-6.7x+2+x^{2}$$

The equation is in standard form.

$$\left(-x^{2}\right)a=x^{2}-\frac{67x}{10}+y+2$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{x^{2}-\frac{67x}{10}+y+2}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$a=\frac{x^{2}-\frac{67x}{10}+y+2}{-x^{2}}$$

Divide y+x^{2}-\frac{67x}{10}+2 by -x^{2}.

$$a=-1+\frac{\frac{67x}{10}-y-2}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{36.89-8a-4y-4ay}-6.7}{2\left(a+1\right)}\text{; }x=\frac{\sqrt{36.89-8a-4y-4ay}+6.7}{2\left(a+1\right)}\text{, }&a\neq -1\\x=\frac{10y+20}{67}\text{, }&a=-1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{36.89-8a-4y-4ay}-6.7}{2\left(a+1\right)}\text{; }x=\frac{\sqrt{36.89-8a-4y-4ay}+6.7}{2\left(a+1\right)}\text{, }&\left(a<-1\text{ or }y\leq \frac{36.89-8a}{4\left(a+1\right)}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq -1\right)\text{ and }\left(a>-1\text{ or }\left(a\neq -1\text{ and }y\geq \frac{36.89-8a}{4\left(a+1\right)}\right)\right)\\x=\frac{10y+20}{67}\text{, }&a=-1\end{matrix}\right.$$