Solve Completing Square Problem: ((x2)/18)-(x/9)=1

[wellyn]

help I am stumped on this ((x²)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)

 

[MarkFL]

Re: competing the square

help I am stumped on this ((x²)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)

We are given:

\(\displaystyle \frac{x^2}{18}-\frac{x}{9}=1\)

I think I would first multiply through by the lowest common denominator to get rid of the denominators. So, multiplying through by 18, we get:

\(\displaystyle x^2-2x=18\)

Can you proceed?

 

[wellyn]

Re: competing the square

no sorry I am stumped

 

[MarkFL]

Re: competing the square

no sorry I am stumped

You want to take half the coefficient of the linear term (the term with $x$ as a factor) and square it, and add this to both sides. What do you get?

 

[CellCoree]

Hello! Completing the square is a technique used to rewrite a quadratic equation in a standard form, which is (x-h)^2 = k. In this case, we have ((x^2)/18)-(x/9)=1. To solve this problem, we need to follow these steps:

Step 1: Factor out the coefficient of x^2, which is 1/18. This gives us (1/18)(x^2-x/9)=1.

Step 2: Take half of the coefficient of x, which is -1/9, and square it. This gives us (-1/9)^2=1/81.

Step 3: Add this value to both sides of the equation. This gives us (1/18)(x^2-x/9+1/81)=1+1/81.

Step 4: Rewrite the left side of the equation as a perfect square. This gives us (1/18)(x-1/9)^2=82/81.

Step 5: Multiply both sides by 18 to eliminate the fraction. This gives us (x-1/9)^2=82.

Step 6: Take the square root of both sides. This gives us x-1/9=±√82.

Step 7: Add 1/9 to both sides to isolate x. This gives us x=1/9±√82.

Therefore, the solutions to this equation are x=1/9+√82 and x=1/9-√82. I hope this helps!