Spot a quadratic equation, write a word problem as one, and solve it by splitting the middle term. Then check each root, and decide which roots make sense for the problem.
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Created by StemPy LabA quadratic equation has the form ax² + bx + c = 0, with a not equal to 0. Expand and simplify before you decide, because a squared term can cancel. A root is a value of x that makes the left side equal to 0, and you can test it by putting it in.
To solve a quadratic equation by factorisation, split the middle term into two parts whose product equals a times c, factorise by grouping, and set each factor equal to 0. Check each root in the original equation. Never divide both sides by x: a root can be lost.
Many problems about areas, numbers, speeds and ages lead to a quadratic equation. Name the unknown, write the equation, put it in standard form, solve it, and then keep only the roots that make sense: a length or an age cannot be negative.
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