You can
put this solution on YOUR website!# 1
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve
( notice
,
, and
)
Plug in a=1, b=-7, and c=-1
Negate -7 to get 7
Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because
.)
Multiply
to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this
solver)
Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
or
Now break up the fraction
or
Simplify
or
So these expressions approximate to
or
So our solutions are:
or
Notice when we graph
, we get:
when we use the root finder feature on a calculator, we find that
and
.So this verifies our answer
# 2
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve
( notice
,
, and
)
Plug in a=1, b=-4, and c=-4
Negate -4 to get 4
Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because
.)
Multiply
to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this
solver)
Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
or
Now break up the fraction
or
Simplify
or
So these expressions approximate to
or
So our solutions are:
or
Notice when we graph
, we get:
when we use the root finder feature on a calculator, we find that
and
.So this verifies our answer
# 3
Start with the given equation
Subtract 9x from both sides
Factor the left side
Now set each factor equal to zero:
or
or
Now solve for x in each case
So our answer is
or
Notice if we graph
we can see that the roots are
and
. So this visually verifies our answer.
(