Unit 8, Lesson 3
Solving Quadratic Equations by Reasoning
Algebra 1
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How many solutions does each equation have? What are the solution(s)? Be prepared to explain how you know.
Each of these equations has two solutions. What are they? Explain or show your reasoning.
Some quadratic equations can be solved by performing the same operation on each side of the equal sign and reasoning about which values for the variable would make the equation true.
Suppose we wanted to solve . We can proceed like this:
and
This means that both and make the equation true and are solutions to the equation.
Many quadratic equations have 2 solutions, but some have only 1 or no solution.