Solution/s:
One way of solving quadratic equation is through factoring.
Lets identify a, b and c first.
What is a? Its 1.
What is b? Its -7.
What is c? Its -8.
Now we know the a,b, and c; we wanted the factors of c such that when added results as b:
The condition is [tex] c = c_1 \cdot c_2, b = c_1 + c_2 [/tex]
The factors of c that makes the above condition true is -8 and 1.
Check:
[tex] -8 = 1 \cdot -8, -7 = 1 - 8 [/tex]
Now we can factor as follows (note that [tex]a[/tex] is 1 here):
[tex] ax^2 + bx + c = (x + c_1)(x + c_2) [/tex]
[tex] x^2 -7x -8 = (x + 1)(x - 8)[/tex]
Now equate the factors to zero, something like this:
[tex] (x + 1 = 0)(x - 8 = 0) [/tex]
Then we solve as follows:
[tex] x + 1 = 0 [/tex]
[tex] \boxed{x = -1} [/tex]
[tex] x - 8 = 0 [/tex]
[tex] \boxed{x = 8} [/tex]
Answer: [tex] x = -1, 8 [/tex]
