Rewrite the function by completing the square g(x)=2x^-7x+5

1. Start with the original function:
g(x) = 2x^2 - 7x + 5

2. Factor out the coefficient of x^2 from the first two terms:
g(x) = 2(x^2 - \frac{7}{2}x) + 5

3. To complete the square, take half the coefficient of x, square it, and add and subtract this inside the parenthesis:
g(x) = 2(x^2 - \frac{7}{2}x + \left(\frac{-7}{4}\right)^2 - \left(\frac{-7}{4}\right)^2) + 5
g(x) = 2(x^2 - \frac{7}{2}x + \frac{49}{16} - \frac{49}{16}) + 5

4. Simplify inside the parenthesis:
g(x) = 2\left((x - \frac{7}{4})^2 - \frac{49}{16} \right) + 5

5. Distribute the 2 and combine constants:
g(x) = 2(x - \frac{7}{4})^2 - 2 \cdot \frac{49}{16} + 5
g(x) = 2(x - \frac{7}{4})^2 - \frac{49}{8} + 5
g(x) = 2(x - \frac{7}{4})^2 - \frac{49}{8} + \frac{40}{8}
g(x) = 2(x - \frac{7}{4})^2 - \frac{9}{8}

Answer:
g(x) = 2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}