Questions: Solve for v, (v-5)^2=2 v^2-11 v+13 If there is more than one solution, separate them with commas. v=

Solution Steps

We start with the equation given in the problem: \[ (v - 5)^{2} = 2v^{2} - 11v + 13 \]

To solve for \( v \), we rearrange the equation by moving all terms to one side: \[ (v - 5)^{2} - (2v^{2} - 11v + 13) = 0 \] This simplifies to: \[ -2v^{2} + 11v + (v - 5)^{2} - 13 = 0 \]

The rearranged polynomial can be factored as follows: \[

• \left(v - 4\right) \left(v + 3\right) = 0 \]

Setting the factored expression equal to zero gives us the solutions: \[ v - 4 = 0 \quad \text{or} \quad v + 3 = 0 \] Thus, we find: \[ v = 4 \quad \text{or} \quad v = -3 \]

Final Answer