To finish our problem we need to
solve the quadratic equation 4x
squared minus 9x
minus 28 equals 0.
We can do this using the
quadratic formula, which
says the roots r1 and r2
of a quadratic equation, 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.
Where are a, b, and c, here, are
4, negative 9, and negative 20.
Which when we put into
the formula gives us
negative negative
9 plus or minus
the square root of negative 9
squared minus 4 times 4 times
negative 28 all over 4 times 2.
Now, we can reduce this, because
negative negative 9 is 9,
negative 9 squared is 81,
negative 4 times 4 times
negative 28 is positive
448, and 2 times 4 is 8.
Now, adding what's under the
square root we get 81 plus 448
is 529, whose square root is 23.
So we have 9 plus or
minus 23 over eight.
9 plus 23 is 32, which
we have over eight.
And 9 minus 23 is negative
14, which we have over 8.
Reducing these we get
4 and negative 7/4.
So we can conclude that
the solutions to 4x
squared minus 9x minus 28
equals 0, are x equals 4
or negative 7/4.
