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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