Solve using factorization method:

Question

x2+7x+10=0

Answer 1

well two times five is ten
and two plus five is 7
so we have it made
(x+2)(x+5) = 0
that works if x+5 = 0 so x = -5
and it works if x+2 = 0 so x = -2

Answer 2

x² + 7 x + 10 = 0

The first term is, x² its coefficient is 1
The middle term is, +7 x its coefficient is 7

The last term, the constantis +10

Multiply the coefficient of the first term by the constant 1 • 10 = 10

Find two factors of 10 whose sum equals the coefficient of the middle term, which is 7

- 10 • ( - 1 ) = 10

- 10 + ( - 1 ) = - 10 - 1 = - 11

- 5 • ( - 2 ) = 10

- 5 + ( - 2 ) = - 5 - 2 = - 7

- 2 • ( - 5 ) = 10

- 2 + ( - 5 ) = - 2 - 5 = - 7

- 1 • ( - 10 ) = 10

- 1 + ( - 10 ) = - 1 - 10 = - 11

1 • 10 = 10

1 + 10 = 11

2 • 5 = 10

2 + 5 = 7

That's it 2 and 5

Rewrite the polynomial splitting the middle term using the factors 2 and 5

x² + 2 x + 5 x + 10 = 0

( x² + 2 x ) + ( 5 x + 10 ) = 0

x • ( x + 2 ) + 5 • ( x + 2 ) = 0

( x + 2 ) • x + ( x + 2 ) • 5 = 0

( x + 2 ) • ( x + 5 ) = 0

x + 2 = 0

x = - 2

x + 5 = 0

x = - 5

The solutions are:

x = - 5 and x = - 2