Question

X^2-7x-6=0
solve using the quadratic formula show all steps

Answer 1

To solve the quadratic equation x^2-7x-6=0, we apply the quadratic formula and find the two solutions to be x = (7 + √(73))/2 and x = (7 - √(73))/2.

Step-by-step explanation:

The quadratic equation x^2-7x-6=0 can be solved using the quadratic formula, which is x = (-b ± √(b^2-4ac))/(2a) for a quadratic equation in the form ax^2+bx+c = 0. In this equation, a = 1, b = -7, and c = -6.

Using these values, we get the following steps:

1. Calculate the discriminant: √((-7)^2 - 4*1*(-6)) = √(49 + 24) = √(73)
2. Apply the quadratic formula:

• x = (-(-7) ± √(73)) / (2*1)
• x = (7 ± √(73)) / 2

Thus, the two solutions for x are x = (7 + √(73))/2 and x = (7 - √(73))/2.

This gives us the two possible values for x.