Solve the following equation algebraically:
[tex]5 x^2=60[/tex]
a. [tex]x \approx \pm 3,46[/tex]
b. [tex]x \approx 3.46[/tex]
c. [tex]x=12[/tex]
d. [tex]x= \pm 12[/tex]
Answer (2)
The solutions to the equation 5 x 2 = 60 are approximately x ≈ ± 3.46 , which corresponds to option (a).
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Divide both sides of the equation by 5 to isolate x 2 : x 2 = 12
Take the square root of both sides: x = ± 12
Simplify the square root: x = ± 2 3
Approximate the value: x ≈ ± 3.46
The final answer is x ≈ ± 3.46 .
Explanation
Isolating x^2 We are given the equation 5 x 2 = 60 and asked to solve for x . We need to isolate x 2 first.
Dividing by 5 Divide both sides of the equation by 5: 5 5 x 2 = 5 60 x 2 = 12
Taking the Square Root Now, take the square root of both sides of the equation to solve for x :
x = ± 12
Simplifying the Square Root Simplify the square root. Since 12 = 4 × 3 , we have 12 = 4 × 3 = 4 × 3 = 2 3 . Therefore, x = ± 2 3 .
Approximating the Value Approximate the value of 2 3 . Since 3 ≈ 1.732 , we have 2 3 ≈ 2 × 1.732 = 3.464 . Therefore, x ≈ ± 3.464 .
Selecting the Correct Answer Comparing our solution x ≈ ± 3.464 to the answer choices, we see that option A, x ≈ ± 3.46 , is the closest.
Examples
Imagine you are designing a square garden and have 60 square feet of space to work with, but only 5/6 of the garden will be used for planting. This equation helps you determine the length of each side of the planting area. By solving for x , you find the dimensions that fit within your available space, ensuring efficient use of your garden plot. This is a practical application of quadratic equations in everyday planning and design.
