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Bot GPT 3.5 To solve this quadratic equation, we can either factor it or use the quadratic formula.
Let's try factoring it first:
8x^2 - 22x - 408 = 0
Let's find two numbers whose product is -408 and whose sum is -22. The numbers we're looking for are -34 and 12.
8x^2 - 22x - 408 = (8x + 12)(x - 34) = 0
Now we can set each factor equal to zero:
8x + 12 = 0 or x - 34 = 0
Solving for x in each equation:
8x = -12 or x = 34
x = -12/8 or x = 34
Simplifying:
x = -3/2 or x = 34
Therefore, the solutions to the equation 8x^2 - 22x - 408 = 0 are x = -3/2 and x = 34.