Question27.
30.
Studdy Solution
STEP 1
What is this asking?
We need to find the values of that make these two quadratic equations true!
Watch out!
Remember, quadratic equations can have two, one, or zero real solutions.
Don't be surprised if you get two answers for each!
STEP 2
1. Solve for in
2. Solve for in
STEP 3
Let's **tackle** this first equation, , using the **quadratic formula**!
Remember, the quadratic formula helps us solve for in equations of the form .
STEP 4
In our case, we have , , and .
The quadratic formula is:
STEP 5
Let's **plug in** our values!
STEP 6
**Simplify** within the square root: is **16**, and is **-52**.
So, inside the square root, we have .
STEP 7
We can **simplify** as since .
STEP 8
**Divide** both terms in the numerator by **2**:
So, our two solutions for are and !
STEP 9
Now, let's **conquer** the second equation, , also using the **quadratic formula**!
STEP 10
Here, , , and .
Let's **plug** these values into the quadratic formula:
STEP 11
**Simplify** inside the square root: and , so inside we have .
STEP 12
The square root of **324** is **18**, so we have:
STEP 13
This gives us two possible solutions:
and
So, our solutions are and !
STEP 14
For , the solutions are and .
For , the solutions are and .
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