Solve the following equation algebraically:
[tex]2 x^2=50[/tex]
A. [tex]\pm 0.2[/tex]
B. [tex]\pm 7.07[/tex]
C. [tex]\pm 5[/tex]
D. [tex]\pm 12.5[/tex]
Answer (2)
To solve 2 x 2 = 50 , we first divide by 2 to get x 2 = 25 and then take the square root, yielding the solutions x = ± 5 . The correct option is C: ± 5 .
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Divide both sides of the equation by 2: x 2 = 25 .
Take the square root of both sides: x = ± 25 .
Simplify the square root: x = ± 5 .
The solutions are ± 5 .
Explanation
Understanding the Problem We are given the equation 2 x 2 = 50 and asked to solve for x algebraically. This means we need to isolate x on one side of the equation.
Isolating x 2 First, we divide both sides of the equation by 2 to get x 2 by itself: 2 2 x 2 = 2 50 x 2 = 25
Solving for x Next, we take the square root of both sides of the equation to solve for x . Remember that when we take the square root of a number, we need to consider both the positive and negative roots: x = ± 25 Since 25 = 5 , we have: x = ± 5
Final Answer Therefore, the solutions to the equation 2 x 2 = 50 are x = 5 and x = − 5 .
Examples
Imagine you are designing a square garden and you have 50 square feet of space available. The equation 2 x 2 = 50 can help you determine the length of each side of the garden if you divide the garden into two equal square sections. Solving this equation gives you the side length, ensuring you utilize the available space efficiently. This type of problem arises in various scenarios, such as determining dimensions in architecture, optimizing space in interior design, or even in basic home improvement projects.
