Answer :
To solve the equation \( 2x^2 = 50 \) algebraically, follow these steps:
1. Isolate \( x^2 \):
Start by dividing both sides of the equation by 2 to isolate \( x^2 \):
[tex]\[ x^2 = \frac{50}{2} \][/tex]
2. Simplify the division:
Perform the division:
[tex]\[ x^2 = 25 \][/tex]
3. Solve for \( x \):
To find the values of \( x \), take the square root of both sides of the equation:
[tex]\[ x = \pm \sqrt{25} \][/tex]
4. Calculate the square root:
The square root of 25 is 5. Therefore:
[tex]\[ x = \pm 5 \][/tex]
Thus, the solutions to the equation \( 2x^2 = 50 \) are \( x = 5 \) and \( x = -5 \).
Now, let’s match these solutions to the provided choices:
a. \( \pm 0.2 \)
b. \( \pm 7.07 \)
c. \( \pm 5 \)
d. \( \pm 12.5 \)
The correct choice that fits \( x = \pm 5 \) is:
c. \( \pm 5 \)
Therefore, the best answer is:
C
1. Isolate \( x^2 \):
Start by dividing both sides of the equation by 2 to isolate \( x^2 \):
[tex]\[ x^2 = \frac{50}{2} \][/tex]
2. Simplify the division:
Perform the division:
[tex]\[ x^2 = 25 \][/tex]
3. Solve for \( x \):
To find the values of \( x \), take the square root of both sides of the equation:
[tex]\[ x = \pm \sqrt{25} \][/tex]
4. Calculate the square root:
The square root of 25 is 5. Therefore:
[tex]\[ x = \pm 5 \][/tex]
Thus, the solutions to the equation \( 2x^2 = 50 \) are \( x = 5 \) and \( x = -5 \).
Now, let’s match these solutions to the provided choices:
a. \( \pm 0.2 \)
b. \( \pm 7.07 \)
c. \( \pm 5 \)
d. \( \pm 12.5 \)
The correct choice that fits \( x = \pm 5 \) is:
c. \( \pm 5 \)
Therefore, the best answer is:
C
