Answer:
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
