Solve for yy. Express your answer as an integer or integers or in simplest radical form.2, minus, y, squared, equals, minus, 142−y 2 =−14

1. Break Down the Problem

We need to solve the equation $2 - y^2 = -14$ for $y$.

2. Relevant Concepts

To solve for $y$, we will first isolate $y^2$ on one side of the equation and then solve for $y$ itself.

3. Analysis and Detail

• Start with the equation: $2 - y^2 = -14$

• Move $2$ to the right side by subtracting $2$ from both sides: $-y^2 = -14 - 2$

• Simplify the right side: $-y^2 = -16$

• Multiply both sides by $-1$ to solve for $y^2$: $y^2 = 16$

• Take the square root of both sides to solve for $y$: $y = \pm 4$

4. Verify and Summarize

Both $y = 4$ and $y = -4$ satisfy the original equation as substituting either value back into the equation $2 - y^2 = -14$ results in true statements.

Final Answer

The solutions are $y = 4$ and $y = -4$.