Question

James is solving the equation x^2+10x=50 by completing the square. What number must be added to both sides of the equation to complete the square?

Answer 1

Let f (x) be a quadratic equation of the form:

$x^2+bx+c$

Where b and c are real numbers.

So a generic procedure for completing squares is:

1) identify b

In this case b = 10

2) divide b between 2 and then square it

$(\frac{b}{2})^ 2$

$(\frac{10}{2})^ 2=25$

3) Add and subtract $b ^ 2$ in the equation

$x ^2+10x + 25 - 25 = 50$

$x ^ 2 + 10x +25 = 75$

4) Rewrite the equation as follows

$(x+\frac{b}{2})^2=c$

$(x + 5) ^ 2 = 75$

The number that you must add to both sides of the equation is number $25 = (\frac{b}{2})^2$