Question

Solve this equation, check all solution. 4a²+19=68

Answer 1

`4a^2+19=68`

Start by substracting 19 on both sides

`\begin{gathered} 4a^2+19=68 \\ 4a^2+19-19=68-19 \\ 4a^2=49 \end{gathered}`

Continue by dividing by 4 on both sides

`\begin{gathered} (4)/(4)a^2=(49)/(4) \\ a^2=(49)/(4) \end{gathered}`

Finalize taking square root on both sides

`\begin{gathered} \sqrt[]{a^2}=\sqrt[]{(49)/(4)} \\ a=(7)/(2) \end{gathered}`

Check answer by replacing a into the first equation

`\begin{gathered} 4\cdot((7)/(2))^2+19=68 \\ 4\cdot((49)/(4))+19=68 \\ 49+19=68 \\ 68=68 \end{gathered}`

solution is correct.