Question

The area of a square is represented by the function:f(x)= 9x^2 + 96x + 256What is the length of one side of the square in terms of x?

Answer 1

x = 5.33

Explanation:

`\begin{gathered} \text{The area of a square is represented by the function below} \\ f(x)=9x^2\text{ + 96x + 256} \\ \text{The standard form of a quadratic function is given as} \\ ax^2\text{ + bx + c = 0} \\ \text{let a = 9, b = 96 and c = 256} \\ \text{Uisng the general formula} \\ x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ x\text{ = }\frac{-(96)\text{ }\pm\text{ }\sqrt[]{96^2\text{ - 4 }\cdot\text{ 9 }\cdot\text{ 256}}}{2\cdot\text{ 9}} \\ x\text{ = }\frac{-96\pm\sqrt[]{9216\text{ - 9216}}}{18} \\ x\text{ = }\frac{-96\text{ }\pm\sqrt[]{0}}{18} \\ x\text{ = }\frac{-96\text{ }\pm0}{18} \\ x\text{ = }\frac{-96\text{ - 0}}{18}\text{ or }\frac{-96\text{ + 0}}{18} \\ x\text{ = }(-96)/(18) \\ x\text{ = -5.33} \\ \text{ since the length of the square can't be negative, hence, x = 5.33} \end{gathered}`