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Answer the questions below.
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Use the quadratic formula to answer the questions below.
Quadratic Formula is x= −b ±b2−4ac√2a
The equation is 2x2+22x+60
Fill in the blanks below (yellow boxes).
(1 point)
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Directions:
Answer the questions below.
You will be able to check your answers by clicking on "Check Answers" at the bottom.
Check your answers as you work.
Treat this like a test review
We encourage you to score at least 70% before submitting so you feel prepared for your unit test.
Use the quadratic formula to answer the questions below.
Quadratic Formula is x= −b ±b2−4ac√2a
The equation is 2x2+22x+60
Fill in the blanks below (yellow boxes).
(1 point)
Skip to navigation
Answers
GPT-4o mini
To solve the quadratic equation \(2x^2 + 22x + 60 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we first need to identify the coefficients \(a\), \(b\), and \(c\).
In this equation:
- \(a = 2\)
- \(b = 22\)
- \(c = 60\)
Next, we can proceed to calculate \(b^2 - 4ac\).
1. Calculate \(b^2\):
\[
b^2 = (22)^2 = 484
\]
2. Calculate \(4ac\):
\[
4ac = 4 \cdot 2 \cdot 60 = 480
\]
3. Now, we substitute these values into the discriminant:
\[
b^2 - 4ac = 484 - 480 = 4
\]
Now, we can use the quadratic formula to find \(x\):
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-22 \pm \sqrt{4}}{2 \cdot 2}
\]
\[
= \frac{-22 \pm 2}{4}
\]
Now we calculate the two possible values for \(x\):
**First solution**:
\[
x = \frac{-22 + 2}{4} = \frac{-20}{4} = -5
\]
**Second solution**:
\[
x = \frac{-22 - 2}{4} = \frac{-24}{4} = -6
\]
Thus, the solutions to the quadratic equation \(2x^2 + 22x + 60 = 0\) are:
\[
x = -5 \quad \text{and} \quad x = -6
\]
Make sure to fill in the yellow boxes with the values determined along the way, namely the values of \(a\), \(b\), \(c\), the discriminant \(b^2 - 4ac\), and the two solutions \(x_1\) and \(x_2\).
In this equation:
- \(a = 2\)
- \(b = 22\)
- \(c = 60\)
Next, we can proceed to calculate \(b^2 - 4ac\).
1. Calculate \(b^2\):
\[
b^2 = (22)^2 = 484
\]
2. Calculate \(4ac\):
\[
4ac = 4 \cdot 2 \cdot 60 = 480
\]
3. Now, we substitute these values into the discriminant:
\[
b^2 - 4ac = 484 - 480 = 4
\]
Now, we can use the quadratic formula to find \(x\):
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-22 \pm \sqrt{4}}{2 \cdot 2}
\]
\[
= \frac{-22 \pm 2}{4}
\]
Now we calculate the two possible values for \(x\):
**First solution**:
\[
x = \frac{-22 + 2}{4} = \frac{-20}{4} = -5
\]
**Second solution**:
\[
x = \frac{-22 - 2}{4} = \frac{-24}{4} = -6
\]
Thus, the solutions to the quadratic equation \(2x^2 + 22x + 60 = 0\) are:
\[
x = -5 \quad \text{and} \quad x = -6
\]
Make sure to fill in the yellow boxes with the values determined along the way, namely the values of \(a\), \(b\), \(c\), the discriminant \(b^2 - 4ac\), and the two solutions \(x_1\) and \(x_2\).