Question

Rewrite the equation by completing the square.

Answer 1

Answer:

$(x-\frac{1}{2})^2=\frac{81}{4}$

Step-by-step explanation:

Hi there!

$x^2-x-20=0$

This equation is written in the form $ax^2+bx+c=0$. First, use partial factoring:

$(x^2-x)-20=0$

For x^2-x, the b value is -1 in $ax^2+bx+c$. To complete the square, take the square of half of 1 and add it in the parentheses as the c value:

$(x^2-x+\frac{1}{2}^2 )-20=0$

However, when adding values to one side of the equation, we must to the same to the other side:

$(x^2-x+\frac{1}{2}^2 )-20=\frac{1}{2}^2$

Complete the square:

$(x-\frac{1}{2})^2-20=\frac{1}{4}$

Move 20 to the other side

$(x-\frac{1}{4})^2=\frac{1}{4}+20\\(x-\frac{1}{2})^2=\frac{81}{4}$

I hope this helps!