Solve the quadratic equation; x^2 + 13x = -40

Answer 1

x^2 + 13x = -40

first of all, these types of problem should be made equal to 0.

example ax^2 + bx + c = 0

after organizing we get:

x^2 + 13x + 40 = 0

now we open 2 parenthesis, because everything is positive in the equation we learn that the signs within the parenthesis are going to be positive.

(x + ?)(x + ?)=0

search for 2 numbers that multiplied returns positive 40.

Posible combinations are:

40*1=40

20*2 = 40

10*4=40

8*5=40

now from this combinations you have to choose the one that by sum of the 2 numbers you multiplied you get the number in the middle of the equation (13). That is 8*5 (8 + 5 = 13)

So the correct combination is

(x+8)(x+5)=0

if you distribute these two parenthesis you get x^2 + 13x + 40 = 0

and that is the way to confirm the combinations are right.