Step-by-step explanation:
[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]
Factor by grouping,
[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]
Complete the square, with the x variables,
[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]
Factor out 25 for the y variables
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]
Complete the square
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]
Simplify the perfect square trinomial
[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]
Make the right side be 1 so divide everything by 25.
[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]
Here our center is (7,2).
