How do you solve sqrt(2a^2-121)=a and check your solution?

Jan 26, 2017

$a = \pm 11$

Explanation:

$a = \sqrt{2 {a}^{2} - 121}$

Square both sides

${a}^{2} = 2 {a}^{2} - 121$

Minus ${a}^{2}$ and add $121$ to both sides

${a}^{2} = 121$

Square root both sides

$a = \pm \sqrt{121} = \pm 11$

Now to check:

$a = \sqrt{2 \times {11}^{2} - 121} = \sqrt{242 - 121} = \sqrt{121} = \pm 11$