To finish our example,
we need to solve
the quadratic
equation 4x squared
minus 37x plus 58 equals 0.
To do this, we can use the
quadratic formula, which
tells us the roots are
1nr2 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 2.
In this example our the
coefficient of x squared is 4.
B, our coefficient
of x, is negative 37.
And c, our constant
coefficient is 58.
So we get that our roots
are negative negative 37
plus or minus the square
root of negative 37
squared minus 4 times 4
times 58, all over 2 times
4, which we can simplify the 37
plus or minus the square root
of 1369 minus 928, all over 8.
Underneath the
square root, we just
have 441 whose
square root is 21.
So we find that our roots of
37 plus or minus 21 over 8,
which can be computed
separately because 37 plus 21
is 58, while 37 minus 21 is
16, which we both have over 8.
Now we can reduce each of these
because 58 over 8 is 29 over 4,
while 16 over 8 is 2.
So we get that the
solutions to 4x
squared minus 37x plus 58
equals 0 are 29 over 4 and 2.
