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Use the quadratic formula to solve 2x^2 - 5x - 1 = 0. Are there multiple solutions?

User Alex Wiese
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Final answer:

To solve the equation 2x^2 - 5x - 1 = 0, we use the quadratic formula, where the coefficients are a=2, b=-5, and c=-1, to find two distinct real solutions.

Step-by-step explanation:

To solve the quadratic equation 2x^2 - 5x - 1 = 0 using the quadratic formula, we first identify the coefficients a, b, and c from the equation, where a = 2, b = -5, and c = -1. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). Substituting our values into this formula gives us:

x = (5 ± √((-5)^2 - 4(2)(-1))) / (2(2))

x = (5 ± √(25 + 8)) / 4

x = (5 ± √(33)) / 4

Thus, we have two possible solutions for x, which are:

x = (5 + √33) / 4

x = (5 - √33) / 4

Therefore, the given quadratic equation has two distinct real solutions.

User Woodley
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