Question

Write an equation for the area and solve the equation for x.

Answer 1

Given the figure of a rectangle

The area = A = 26

Length = x + 6

width = x + 2

Area = length * Width

so, the equation of the area will be:

`A=(x+6)(x+2)`

so,

`(x+6)(x+2)=26`

solve for x as follows:

`\begin{gathered} x^2+8x+12=26 \\ x^2+8x+12-26=0 \\ x^2+8x-14=0 \\ \end{gathered}`

Use the general rule to find the value of x

So,

`\begin{gathered} a=1,b=8,c=-14 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-8\pm\sqrt[]{64-4\cdot1\cdot-14}}{2\cdot1} \\ \\ x=\frac{-8\pm\sqrt[]{120}}{2}=\frac{-8\pm2\sqrt[]{30}}{2}=-4\pm\sqrt[]{30} \end{gathered}`

So, the answer will be:

`\begin{gathered} A=(x+6)(x+2)_{} \\ \\ x=-4+\sqrt[]{30},-4-\sqrt[]{30} \end{gathered}`