Solving quadratic equations
A quadratic equation
is an equation whose sides are both polynomials of degree at most 2.
Quadratic equations in one variable can always be solved using this method:
- Simplify both sides (if necessary).
- If there are any variable terms on the right-hand side,
then subtract these terms from both sides (and simplify).
- If there are no variables left in the equation,
then you have a statement that is always true or always false,
and that is your final answer.
Otherwise …
- If there is a constant term on the left-hand side,
then subtract this term from both sides (and simplify).
- If there is now a coefficient and/or a minus sign
on the leading term on the left-hand side,
then divide both sides by that coefficient or −1 (and simplify).
- If the left-hand side is linear, then you should have the answer now.
Otherwise …
- If there is more than one term on the left-hand side,
then add a constant to both sides
that makes the left-hand side into a perfect square.
- If there is more than one term on the left-hand side,
then factor the left-hand side (while you simplify the right-hand side).
- Take square roots of both sides
(and simplify with ± on the right-hand side).
- If there is now a constant term on the left-hand side,
then subtract this term from both sides (and simplify).
At this point, you should have the answer.
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This web page was written between 2007 and 2016 by Toby Bartels,
last edited on 2016 July 22.
Toby reserves no legal rights to it.
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