Question
Solve the equation using the quadratic formula.
The solution set is { }.
(Simplify your answer. Type an exact answer, using radicals and
as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers
as needed.)
(Simplify your answer. Type an exact answer, using radicals and
as needed.)
Ask by Rodriguez Chan. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are
and
.
Solution
We start with the quadratic equation
The quadratic formula is
Here,
,
, and
.
Substitute these values into the formula:
Simplify step by step:
- Compute
:
- Compute the discriminant
:
- Substitute the discriminant back into the formula:
- Simplify
using :
- Write the expression for
:
- Divide numerator by 2:
Thus, the solution set is
.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To use the quadratic formula, we start with the standard format of a quadratic equation
. For the equation
, we have:
The quadratic formula is given by:
First, we calculate the discriminant
:
Since the discriminant is negative, the solutions will involve imaginary numbers. Now we substitute into the quadratic formula:
Simplifying
:
Now we can simplify the expression further:
Thus, the solution set is: