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

Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

x = 5plus or minus StartRoot 31 EndRoot

x = 5plus or minus StartRoot 19 EndRoot

x = 5plus or minus 2 StartRoot 19 EndRoot

x = 5plus or minus 2 StartRoot 31 EndRoot

the answer is a x = 5 + √31 amd x = 5 - √31

x = 5 + √31 amd x = 5 - √31

Step-by-step explanation:

Rewrite 6 = x2 - 10x using " ^ " to denote exponentiation. Then re-arrange the terms in descending powers of x:

x^2 - 10x - 6 = 0

Let's solve this by completing the square. Add 25 to both sides and simplify the result:

x^2 - 10x + 25 = 6 + 25 = 31

The first three terms can be rewritten as

(x - 5) ^2

and so we now have (x - 5) ^2 = 31.

Taking the sqrt of both sides, we get

x - 5 = ± √31

And so the two real, unequal roots are

x = 5 + √31 amd x = 5 - √31