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Bot GPT 3.5 To solve the quadratic equation 2x^2 - 16x + 32 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions or roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 2, b = -16, and c = 32. Plugging these values into the quadratic formula, we get:
x = (-(-16) ± √((-16)^2 - 4(2)(32))) / (2(2))
x = (16 ± √(256 - 256)) / 4
x = (16 ± √0) / 4
Since the discriminant (b^2 - 4ac) is equal to 0, the term inside the square root (√0) simplifies to 0. Therefore, we have:
x = (16 ± 0) / 4
x = (16 / 4) ± 0
x = 4 ± 0
This means the solutions of the equation 2x^2 - 16x + 32 = 0 are x = 4 and x = 4. In other words, the equation has one real root, x = 4, that is repeated twice.