Question

Simplify the following equations in ax^2+bx+c=0 or ay^2+c=0 2x+y=6 4x^2+5y+y+1=0

Answer 1

Given the equation;

`4x^2+5y^2+y+1=0`

We shall begin by Subtracting 5y^2 + y from both sides;

`\begin{gathered} 4x^2+5y^2+y+1-5y^2-y=0-5y^2-y \\ 4x^2+1=-5y^2-y \\ \text{Factor out -1 from the right hand side;} \\ 4x^2+1=-1(5y^2+y) \end{gathered}`

Next step we subtract 1 from both sides;

`\begin{gathered} 4x^2+1-1=-1(5y^2+y)-1 \\ 4x^2=-(5y^2+y)-1 \\ \end{gathered}`

Next step we take the square root of both sides;

`\begin{gathered} \sqrt[]{4x^2}=\pm\sqrt[]{-(5y^2+y)-1} \\ 2x=\pm\sqrt[]{-(5y^2+y)-1} \end{gathered}`

We can now open the parenthesis on the right hand side;

`\begin{gathered} 2x=\pm\sqrt[]{-5y^2-y-1} \\ \text{Divide both sides by 2;} \\ x=\frac{\pm\sqrt[]{-5y^2-y-1}}{2} \end{gathered}`