Question

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.

Answer 1

Complete the square on x by adding​ 49 to both sides.

Complete the square on y by adding​ 81 to both sides.

Explanation:

We have been given an equation
`(x^2+14x)+(y^2+18y)=5`. 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.

`((14)/(2))^2=7^2=49`

`((18)/(2))^2=9^2=81`

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:

`(x^2+14x+49)+(y^2+18y+81)=5+49+81`

Applying the perfect square formula
`a^2+2ab+b^2=(a+b)^2`, we will get:

`(x+7)^2+(y+9)^2=135`

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.