Question

What constant term should be added to both sides to complete the square on the left side? x 2 - x + _____ = 10

Answer 1

Answer:

The required term is $(\frac{1}{2})^2$          

Step-by-step explanation:

Given : Equation $x^2-x+.....=10$

To find : What constant term should be added to both sides to complete the square on the left side?

Solution :

The quadratic equation is in the form $ax^2+bx+c=0$

To complete the square we have to add the term $(\frac{b}{2})^2$

If we compare the equation, b=-1

So, The term has to add is $(\frac{-1}{2})^2=(\frac{1}{2})^2$

Substitute the term in the equation as adding it on both side,

$x^2-x+(\frac{1}{2})^2=10+(\frac{1}{2})^2$

Now, we solve to make a complete square,

$(x-\frac{1}{2})^2=10+\frac{1}{4}$

$(x-\frac{1}{2})^2=\frac{41}{4}$

Therefore, The required term is $(\frac{1}{2})^2$

                                         

Answer 2

x 2 - x + _____ = 10

$x^2+x +( \frac{1}{2} )^2=10+( \frac{1}{2} )^2\\~\\~\\ (x+\frac{1}{2} )^2=10+( \frac{1}{4} )$

I hope that helps!