Question

In simplest radical form, what are the solutions to the quadratic equation 6 = x^2 - 10x?

Quadratic formula: x = ___"
Option a) x = 5 + √31
Option b) x = 51/19
Option c) x = 52/19
Option d) x = 52√31

Answer 1

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

Step-by-step explanation:

To find the solutions to the quadratic equation 6 = x² - 10x in simplest radical form, we can rearrange the equation to the form ax² + bx + c = 0. In this case, a = 1, b = -10, and c = -6. Substituting these values into the quadratic formula, we get:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we have: x = (10 ± √(100 - 4(1)(-6))) / (2(1))

Simplifying further, we get x = (10 ± √(100 + 24)) / 2

x = (10 ± √124) / 2

x = (10 ± 2√31) / 2

Finally, we simplify further by cancelling out the common factor of 2, leaving us with x = 5 ± √31.