Solving Quadratic Equations
A person plants two square plots for garden. the of the areas of both plots is 225 square feet. If the side of one plot is 3 feet longer than the side of the other one, find the length of the smaller plot.
Karin Algebra Class Says:
Let x = the side of the smaller plot.
Since the other plot is 3 feet longer, the second plot's length is x +3.
You know the area of the both plots is 225.
Therefore, we need to find the area of both plots and add them together to get 225.
Remember area of a square is s^2 or the side squared.
Plot 1 area + Plot 2 area = 225
x^2 + (x+3)^2 = 225
x^2 + x^2 + 6x + 9 = 225
Simplify:
2x^2 + 6x + 9 = 225
Now, set the equation equal to 0 by subtracting 225 from both sides.
2x^2 + 6x + 9 - 225 = 225 - 225
2x^2 + 6x -216 = 0
Now use the quadratic formula to solve.
a = 2, b = 6, c = -216
Use the following web page for examples on how to use the quadratic formula:
https://www.algebra-class.com/quadratic-formula.html
Your answer should end up to be 9 for the length of the shorter plot.
Good luck,
Karin