Question

Solve for u, where u is a real number.Square root of -3u + 18 = u

Answer 1

GIVEN

The equation is given to be:

`√(-3u+18)=u`

SOLUTION

To solve for u.

Square both sides of the equation:

`\begin{gathered} -3u+18=u^2 \\ Rearrange \\ u^2+3u-18=0 \end{gathered}`

Solve the quadratic equation by factorization:

`\begin{gathered} u^2+3u-18=0 \\ Rewrite \\ u^2+6u-3u-18=0 \\ Factor \\ u(u+6)-3(u+6)=0 \\ Factor\text{ }again \\ (u+6)(u-3)=0 \\ \mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0 \\ \therefore \\ u+6=0,u=-6 \\ or \\ u-3=0,u=3 \end{gathered}`

Check the solutions if it satisfies the equation:

`\begin{gathered} u=-6 \\ √(-3(-6)+18)=-6 \\ √(36)=-6 \\ 6=-6\text{ \lparen False\rparen} \\ \\ u=3 \\ √(-3(3)+18)=3 \\ √(9)=3 \\ 3=3\text{ \lparen True\rparen} \end{gathered}`

Therefore, the solution to the equation is:

`u=3`