Final answer:
To solve the equation 5x^2 - 3x - 7 = 0 using the quadratic formula, the approximate solutions are x ≈ 1.39 and x ≈ -1.29.
Step-by-step explanation:
To solve the equation 5x^2 - 3x - 7 = 0 using the quadratic formula, we can identify the values of a, b, and c:
a = 5
b = -3
c = -7
Substituting these values into the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / (2a)
we can calculate the solutions for x. Plugging in the values of a, b, and c:
x = [-(-3) ± √((-3)^2 - 4(5)(-7))] / (2(5))
Simplifying further, we get:
x = [3 ± √(9 + 140)] / 10
which becomes:
x = [3 ± √(149)] / 10
Hence, the approximate solutions to the equation are:
x ≈ 1.39 and x ≈ -1.29