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

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 $(x^2+14x)+(y^2+18y)=5$. 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.

$(\frac{14}{2})^2=7^2=49$

$(\frac{18}{2})^2=9^2=81$

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.