Unit 4, Lesson 16
Solving Quadratics
Algebra 2
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The expression
Elena and Han solved the equation
Elena said, “First I added 2 to each side:
So that tells me:
I can find the square roots of both sides:
Which is the same as:
So the two solutions are
Han said, “I used the quadratic formula:
Since
or
So:
I think the solutions are
Do you agree with either of them? Explain your reasoning.
Solve each quadratic equation with a method of your choice. Be prepared to compare your approach with a partner‘s.
Consider the quadratic equation
To complete the square, note that the perfect square
This means the perfect square
The two numbers that square to make
which means the two solutions are:
Now let’s look at another quadratic equation
We could divide each side by 3 and then complete the square like before, but let’s use the quadratic formula:
To use this formula, we first need to put the equation in standard form and identify
so
Evaluating these solutions with a calculator gives decimal approximations -0.281 and 0.948.