Answer:
[tex]x = 5 \± \sqrt{31}[/tex]
Step-by-step explanation:
Given
[tex]6 = x^2 - 10x[/tex]
Required
The solution in radical form
[tex]6 = x^2 - 10x[/tex]
Rewrite as:
[tex]x^2 - 10x - 6 = 0[/tex]
Using the quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
a = 1
b = -10
c = -6
So, we have:
[tex]x = \frac{-(-10) \± \sqrt{(-10)^2 - 4*1*(-6)}}{2*1}[/tex]
[tex]x = \frac{10 \± \sqrt{100 +24}}{2*1}[/tex]
[tex]x = \frac{10 \± \sqrt{124}}{2}[/tex]
Split the roots
[tex]x = \frac{10 \± \sqrt{4 * 31}}{2}[/tex]
Express [tex]\sqrt 4[/tex] as 2
[tex]x = \frac{10 \± 2\sqrt{31}}{2}[/tex]
Split the fraction
[tex]x = \frac{10}{2} \± \frac{2\sqrt{31}}{2}[/tex]
[tex]x = 5 \± \sqrt{31}[/tex]
