$50 x^2=70$
What is one of the solutions to the given equation?
$\sqrt{\frac{7}{5}}$
$\sqrt{\frac{5}{7}}$
$\sqrt{20}$
$2 \sqrt{5}$
Answer (1)
Divide both sides of the equation by 50: x 2 = 50 70 = 5 7 .
Take the square root of both sides: x = ± 5 7 .
Identify the matching solution from the given options.
The solution is: 5 7 .
Explanation
Problem Analysis We are given the equation 50 x 2 = 70 and asked to find one of its solutions from the given options.
Isolating x^2 First, we want to isolate x 2 by dividing both sides of the equation by 50: x 2 = 50 70 Simplifying the fraction, we get: x 2 = 5 7
Solving for x Next, we take the square root of both sides of the equation to solve for x :
x = ± 5 7
Finding the Matching Solution Now, we compare our solutions to the given options. We see that 5 7 is one of the options.
Final Answer Therefore, one of the solutions to the equation 50 x 2 = 70 is 5 7 .
Examples
Imagine you are designing a square garden and need to determine the length of each side. If the area of the garden is represented by 50 x 2 and you know the area must be 70 square feet, solving the equation 50 x 2 = 70 will give you the length x of each side. This problem demonstrates how quadratic equations can be used to solve real-world problems involving areas and dimensions.
