To solve the quadratic equation, let's first write it down clearly based on your description.
The equation is:
\[ 19 + 2x^2 = 21 \]
Next, we need to isolate the \( x^2 \) term. We can do this by subtracting 19 from both sides of the equation:
\[ 2x^2 = 21 - 19 \]
This simplifies to:
\[ 2x^2 = 2 \]
Now, divide both sides by 2:
\[ x^2 = 1 \]
Next, we take the square root of both sides to find \( x \):
\[ x = \pm 1 \]
Thus, the solutions for the quadratic equation are:
\[ x = 1 \quad \text{and} \quad x = -1 \]
In simplest form, the solutions are \( x = 1 \) and \( x = -1 \).