The formula for determining the area of a square is expressed as
Area = length^2
Given that length = x and area = 50, it means that
50 = x^2
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By modelling our equation, we have
x^2 - 50 = 0
It can also be written as
x^2 + 0x - 50 = 0
The general formula for solving quadratic equations is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}\text{ }}{2a} \\ a\text{ = 1, b = 0, c = - 50. thus} \\ x\text{ = }\frac{-\text{ 0 }\pm\sqrt[]{}0^2-4\times1\times-50}{2\times1} \\ x\text{ =}\pm\text{ }\frac{\sqrt[]{200}}{2} \\ x\text{ = }\frac{14.14}{2}\text{ or x = }\frac{-\text{ 14.14}}{2} \\ x\text{ = 7.07 or x = - 7.07} \end{gathered}[/tex]
The length cannot be negative. Thus,
length = 7.07 ft
