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Part 1
Solve the equation for real solutions by the quadratic formula.
3x2−5x−7=0

1 answer

To solve the equation 3x^2 - 5x - 7 = 0 using the quadratic formula, we first identify the coefficients a, b, and c in the general quadratic equation format ax^2 + bx + c = 0.

Comparing the given equation 3x^2 - 5x - 7 = 0 to the general format, we have:
a = 3
b = -5
c = -7

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c, we can solve for x:

x = (-(-5) ± √((-5)^2 - 4(3)(-7))) / (2(3))

Simplifying further:

x = (5 ± √(25 + 84)) / 6
x = (5 ± √(109)) / 6

Therefore, the solutions for the equation 3x^2 - 5x - 7 = 0 are:

x = (5 + √109) / 6
x = (5 - √109) / 6