Question

What number needs to be added to both sides of the equation to complete the square? X^2−7x=5 Enter your answers in the boxes.

Answer 1

ANSWER

We need to add half the coefficient of $x$ all square.

$\frac{49}{4}$

EXPLANATION

Given the equation,

$x^{2} -7x=5$.

We compare to the general equation,

$ax^2+bx+c=0$

This means that;

$a=1,b=-7,c=-5$

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

That is $(\frac{-7}{2})^2=\frac{49}{4}$.

Hence the number to be added to both sides is $\frac{49}{4}$.

Note that before we complete the square, the coefficient of the term in$x^2$ must always be 1.