Question

Nathaniel was completing the square in order to turn the general form of circle into standard form of a circle. His work is shown below. x2 + y2 + 6x – 10y - 2 = 0 x2 + y2 + 6x – 10y = 2 x² + 6x + + y2 – 10y +_ = 2 + + x2 + 6x + 9+ y2 – 10y + = 2 + 9 + Enter the numeric value that will be placed in both blanks to complete his step. I

Answer 1

Given the following expression

$x^2+y^2\text{ + 6x - 10y - 2 = 0}$

Firstly, we need to find the perfect square

$\begin{gathered} \text{Collect the like terms} \\ x^2+6x+y^2\text{ - 10y = 2} \\ \text{ Find the p}\operatorname{erf}ect\text{ square} \\ x^2\text{ + (}\frac{6}{2}x)+y^2\text{ - (}\frac{10}{2}y)\text{ = 2} \\ x^2+3x+(3)^2+y^2-5y+(-5)^2\text{ = 2} \\ x^2+3x+9+y^2\text{ - 5y + 25 = 2} \\ \text{Add p}\operatorname{erf}ect\text{ square to both sides} \\ x^2+6x+y^2\text{ - 5y = 2 + 9 + 25} \end{gathered}$