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?

Question

asked Apr 12, 2019 81.2k views

1 Answer

Enom · Answer 1 · 2019-04-17T13:41:09+0000

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

$((b)/(2))^ 2\\$

$((10)/(2))^ 2=25\\$

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

$(x+(b)/(2))^2=c\\$

$(x + 5) ^ 2 = 75\\$

The number that you must add to both sides of the equation is number
25 = ((b)/(2))^2