In simplest radical form, what are the solutions to the quadratic equation 6 = x² - 10x?

Solution:

The given quadratic equation is:

x² - 10x - 6 = 0

The roots of a quadratic equation of the ax² + bx + c are given by the formula below:

Roots = (-b ± √b² - 4ac)/2a

For the quadratic equation under consideration

a = 1, b = - 10, c = -6

The roots of the equation are:

[-(-10) ± √(-10)² - 4(1)(-6) ]/ 2(1)

= [10 ± (√100 + 24)] / 2

= [10 ± √124] / 2

=  [10 ± √31 × 4 ]/ 2

= [10 ± 2√31] / 2

= 5 ± √31

Hence the two roots are 5 + √31, 5 - √31

---

In simplest radical form, what are the solutions to the quadratic equation 6 = x² - 10x?

Summary:

In simplest radical form, the solutions to the quadratic equation 6 = x² - 10x are 5 + √31, and 5 - √31.