Unit 4, Lesson 16
Solving Quadratics
Algebra 2
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The expression is equivalent to . Which expressions are equivalent to for some number ?
Elena and Han solved the equation in different ways.
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
and ."
Han said, “I used the quadratic formula:
Since , that means , , and . I know:
or
So:
I think the solutions are
and .”
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 . One way to solve equations like this is by completing the square.
To complete the square, note that the perfect square is equal to . Compare the coefficients of in to our expression to see that we want , or just .
This means the perfect square is equal to , so adding to each side of our equation will give us a perfect square.
The two numbers that square to make are and , so:
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 , , and . Rearranging, we get:
so , , and . We have to be careful to pay attention to the negative signs. Using the quadratic formula, we get:
Evaluating these solutions with a calculator gives decimal approximations -0.281 and 0.948.