Solve using factorization method:
x2+7x+10=0
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
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
To solve the quadratic equation using factorization, we need to factorize it into two binomials set equal to zero.
The given equation is: x^2 + 7x + 10 = 0
We need to find two numbers that multiply to give 10 and add up to give 7. These numbers are 2 and 5.
Now, we can rewrite the equation as: (x + 2)(x + 5) = 0
Setting each factor equal to zero, we get:
x + 2 = 0 or x + 5 = 0
Solving both equations separately:
For x + 2 = 0:
x = -2
For x + 5 = 0:
x = -5
Therefore, the solutions to the equation x^2 + 7x + 10 = 0 are x = -2 and x = -5.