Question

use the quadratic formula to answer the questions below
quadratic formula is x = -b+ square b^2 - 4ac/ 2a
the equation is 2x^2 + 22x + 60
fill the blanks below ( yellow boxes )

part A
GCF
The gcf is =
the quadrtic with the factored out the gcf is =
A=
B=
c=
part B use the quadratic formula
x = ---- + ----^2 - 4(-----)(-----)/ 2 (-------)
part c solove for X
x = ------- (lesser number
x = -------- (greater number)

Answer 1

part B is wrong rework it

Answer 2

rework it again for the equation for part B

Answer 3

Let's solve the given problem step by step.

Part A:
1. **Finding the GCF:**
The coefficients of the quadratic equation \(2x^2 + 22x + 60\) are:
- \(2\) (coefficient of \(x^2\))
- \(22\) (coefficient of \(x\))
- \(60\) (constant term)

The GCF of \(2\), \(22\), and \(60\) is \(2\).

2. **Factoring out the GCF:**
If we factor out \(2\), we get:
\[
2(x^2 + 11x + 30)
\]

3. **Values for A, B, and C:**
The factored form yields the new coefficients:
- \(A = 1\) (from \(x^2\))
- \(B = 11\) (from \(11x\))
- \(C = 30\) (the constant term)

So for Part A, we have:
- The GCF is = **2**
- The quadratic with the factored out the GCF is = **2(x^2 + 11x + 30)**
- A = **1**
- B = **11**
- C = **30**

---

Part B:
Using the quadratic formula:
\[
x = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}
\]

Plugging in the values we found:
- A = **1**
- B = **11**
- C = **30**

So, we can fill in:
\[
x = \frac{-11 \pm \sqrt{11^2 - 4(1)(30)}}{2(1)}
\]

Part C:
Now, let's calculate the discriminant and solve for \(x\):
1. Calculate \(B^2 - 4AC\):
\[
B^2 - 4AC = 11^2 - 4 \cdot 1 \cdot 30 = 121 - 120 = 1
\]

2. Now, plugging this into our formula:
\[
x = \frac{-11 \pm \sqrt{1}}{2}
\]
\[
x = \frac{-11 \pm 1}{2}
\]

3. Calculating the two possible values for \(x\):
- For the lesser number:
\[
x = \frac{-11 - 1}{2} = \frac{-12}{2} = -6
\]
- For the greater number:
\[
x = \frac{-11 + 1}{2} = \frac{-10}{2} = -5
\]

So, we have:
- x = **-6** (lesser number)
- x = **-5** (greater number)

---

In summary, the filled blanks are:
- The GCF is = **2**
- The quadratic with the factored out the GCF is = **2(x^2 + 11x + 30)**
- A = **1**
- B = **11**
- C = **30**

- x = **-11** + **sqrt{1}** / **2**
- x = **-6** (lesser number)
- x = **-5** (greater number)

Answer 4

Apologies for the confusion in Part B. Let's carefully apply the quadratic formula to the coefficients provided.

### Given Quadratic Equation
The quadratic equation we are working with is:
\[
2x^2 + 22x + 60
\]

### Step 1: Identify A, B, and C
From our analysis in Part A:
- A = **2**
- B = **22**
- C = **60**

### Step 2: Write the Quadratic Formula
The quadratic formula is given by:
\[
x = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}
\]

### Part B: Substitute A, B, and C into the Formula
Substituting our values of A, B, and C into the quadratic formula:
\[
x = \frac{-22 \pm \sqrt{22^2 - 4 \cdot 2 \cdot 60}}{2 \cdot 2}
\]

### Step 3: Calculate the Discriminant
Now, calculate the discriminant \(B^2 - 4AC\):
\[
22^2 = 484
\]
\[
4 \cdot 2 \cdot 60 = 480
\]
Now, calculating the discriminant:
\[
B^2 - 4AC = 484 - 480 = 4
\]

### Step 4: Substitute the Discriminant Back into the Formula
Now plug the value of the discriminant back into the formula:
\[
x = \frac{-22 \pm \sqrt{4}}{4}
\]

Since \(\sqrt{4} = 2\):
\[
x = \frac{-22 \pm 2}{4}
\]

### Part C: Solve for x
Calculating the two possible values:
1. For the lesser number:
\[
x = \frac{-22 - 2}{4} = \frac{-24}{4} = -6
\]
2. For the greater number:
\[
x = \frac{-22 + 2}{4} = \frac{-20}{4} = -5
\]

### Final Answers for Part B and Part C:
- \( x = -22 + 2 / 4 \)
- x = **-6** (lesser number)
- x = **-5** (greater number)

Thank you for your patience, and I hope this now accurately reflects your needs!

Answer 5

Certainly! Let’s set everything up correctly for Part B of the given quadratic equation \(2x^2 + 22x + 60\) using the quadratic formula properly without any mistakes.

### Part A Recap
From previously discussed calculations, we identified:
- A = **2**
- B = **22**
- C = **60**

### Part B: Using the Quadratic Formula
The correct quadratic formula is:

\[
x = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}
\]

Now substitute the values of A, B, and C into the quadratic formula:

1. **Writing the formula with the values substituted:**
\[
x = \frac{-22 \pm \sqrt{22^2 - 4(2)(60)}}{2(2)}
\]

2. **Calculating the terms in the formula:**
- \(B^2 = 22^2 = 484\)
- Calculate \(4AC\):
\[
4 \cdot 2 \cdot 60 = 480
\]
- Calculating the discriminant:
\[
B^2 - 4AC = 484 - 480 = 4
\]

3. Substituting these values back into the equation:
\[
x = \frac{-22 \pm \sqrt{4}}{4}
\]

4. **Since \(\sqrt{4} = 2\):**
\[
x = \frac{-22 \pm 2}{4}
\]

### Part C: Solving for x
Now, we can solve for x by considering the two cases:
1. **For the lesser root:**
\[
x = \frac{-22 - 2}{4} = \frac{-24}{4} = -6
\]

2. **For the greater root:**
\[
x = \frac{-22 + 2}{4} = \frac{-20}{4} = -5
\]

### Summary of Results
The correct entries for Part B are:
- The quadratic equation with substituted values in the quadratic formula is:
\[
x = \frac{-22 \pm \sqrt{22^2 - 4(2)(60)}}{2(2)}
\]

### Final Answers for Part C:
- x = **-6** (lesser number)
- x = **-5** (greater number)

Thank you for your patience, and I hope this now aligns perfectly with your request!