Q:

In the equation left parenthesis x squared plus 14 x right parenthesis plus left parenthesis y squared minus 18 y right parenthesisequals​5, complete the square on x by adding​ _______ to both sides. Complete the square on y by adding​ _______ to both sides.

Accepted Solution

A:
Answer:Complete the square on x by adding​ 49 to both sides.Complete the square on y by adding​ 81 to both sides.Step-by-step explanation:We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.We know to complete a square, we add the half the square of coefficient of x or y term.Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.[tex](\frac{14}{2})^2=7^2=49[/tex][tex](\frac{18}{2})^2=9^2=81[/tex]Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:[tex](x+7)^2+(y+9)^2=135[/tex]Therefore, We can complete the square on x by adding​ 49 to both sides and the square on y by adding​ 81 to both sides.