Question

If there is more than one solution, separate them with commas.

Answer 1

We need to solve the equation:

`2\\u²-2\\u+60=(\\u-6)²`

Expanding the right side, we obtain:

`2\\u²-2\\u+60=\\u²-12\\u+36`

And applying the same operations on both sides, we obtain:

`\begin{gathered} 2\\u²-2\\u+60-(\\u²-12\\u+36)=\\u²-12\\u+36-(\\u²-12\\u+36) \\ \\ 2\\u²-2\\u+60-\\u²+12\\u-36=0 \\ \\ \\u²+10\\u+24=0 \end{gathered}`

Now, using the quadratic formula, we obtain:

`\begin{gathered} \\u=(-10\pm√(10²-4(1)(24)))/(2(1)) \\ \\ \\u=(-10\pm√(4))/(2) \\ \\ \\u=(-10\pm2)/(2) \\ \\ \\u=-5\pm1 \\ \\ \\u_1=-5-1=-6 \\ \\ \\u_2=-5+1=-4 \end{gathered}`

Answer: ν = -6, -4