To finish our problem, we need
to solve the quadratic equation
x squared plus x minus
2 equals 0, which
we can do using the
quadratic formula, which
says that the roots of ax
squared plus bx plus c equals
0 are given by the
formula negative
b plus or minus the
square root of b
squared minus 4ac all over 2a.
Here, our a, b, and c are our
coefficients of x squared, x,
and the constant.
So a is 1, b is 1 as
well, and c is negative 2,
which, when we put
into our formula,
is negative 1 plus or
minus the square root of 1
squared minus 4 times 1 times
negative 2 all over 2 times
1, which is negative 1 plus
or minus the square root of 1
plus 8, because
negative 4 times 1
is negative 4, which,
multiplied by negative 2,
gives positive 8.
And we're dividing by 2
times 1, which is just 2.
Simplifying what's under
the square root, 1 plus 8
is 9, whose square root is 3.
So we have negative 1
plus or minus 3 over 2.
Negative 1 plus 3 is 2,
which we have over 2.
And negative 1 minus
3 is negative 4,
which we also have over 2.
Reducing these, we
get 1 and negative 2.
So the solutions of x squared
plus x minus 2 equals 0
are x equals 1 and negative 2.
