Find a,b,c a^2+2a^2=19^2

$a^{2} + 2 a^{2} = 19^{2}$

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Add $a^{2}$ and $2 a^{2}$ .

$3 a^{2} = 19^{2}$

Simplify the right side.

Raise $19$ to the power of $2$ .

$3 a^{2} = 361$

Subtract $361$ from both sides of the equation.

$3 a^{2} - 361 = 0$

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a \cdot a^{2} + b a + c$

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 3$ , $b = 0$ , $c = - 361$