Quadratic in Form
An equation is quadratic in form when it can be written in this
standard form
where the same expression is inside both ( )'s.
In other words, if you have
a
times the square of the expression following
b
plus
b
times that same expression not squared plus
c
equal to 0, you have an equation that is
quadratic in form.
If we substitute what is in the ( ) with a variable like
t
, then the original equation will become a
quadratic equation.
Solving Equations that are
Quadratic in Form
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Step 1
:
Write in Standard Form,
, if needed.
andard form, move any term(s) to the appropriate side by using the addition/subtraction property of equality.
Also, make sure that the squared term is written first left to right, the expression not squared is
second and the constant is third and it is set equal to 0.
Step 2
:
Substitute a variable in for the expression that follows
b
in the second
term.
In other words, substitute your variable for what is in the ( ) when it
is in standard form,
.
I’m going to use
t
for my substitution, but really you can use any variable as long as it is not
the variable that is used in the original equation.
Step 3
:
Solve the quadratic equation created in step 2.
If you need a review on solving quadratic equations, feel free to go to
Tutorial 17:
Quadratic Equations
.
You can use any method you want to solve the quadratic equation: factoring, completing the
square or quadratic formula.
Step 4
:
Find the value of the variable from the original equation.
Keep in mind that you are finding a solution to the original equation
and that the variable you substituted in for in step 2 is not your
original variable.
Use the substitution that was used to set up step 2 and then solve for the original variable.
Step 5
:
Check your solutions.
In some cases, you will be working with rational exponents and
square roots in your problems. Those types of equations can cause
extraneous solutions. Recall that an extraneous solution is one that is
a solution to an equation after doing something like raising both sides
of an equation by an even power, but is not a solution to the original
problem.
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 Spring '11
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 Algebra, Quadratic equation, Elementary algebra, Irrational number

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