Final answer:
To solve the equation 2x²=50 algebraically, we can use the quadratic formula. The solutions are ±√(50) / 2, which simplifies to ±5. Therefore, option (c) is the correct answer.
Step-by-step explanation:
This expression is a quadratic equation of the form 2x² - 50 = 0. To solve this equation algebraically, we can apply the quadratic formula.
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / (2a)
Comparing this formula with our equation 2x² - 50 = 0, we can see that a = 2, b = 0, and c = -50.
Substituting these values into the quadratic formula, we get:
x = (-0 ± √(0² - 4 * 2 * -50)) / (2 * 2)
x = ±√(200) / 4 = ±√(4 * 50) / 4 = ±√(4) * √(50) / 4 = ± 2√(50) / 4 = ± √(50) / 2
Simplifying, we have:
x = ± √(50) / 2
The simplified solution is option (c) ±5.