Question
or
Solve the quadratic equation.
7x2+3x–1=0
Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes.
Answers
GPT-4o mini
To solve the quadratic equation \(7x^2 + 3x - 1 = 0\), we can use the quadratic formula:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
where \(a = 7\), \(b = 3\), and \(c = -1\).
First, we calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 3^2 - 4 \cdot 7 \cdot (-1) = 9 + 28 = 37
\]
Since the discriminant is positive, there are two real solutions.
Now, we can substitute the values into the quadratic formula:
\[
x = \frac{{-3 \pm \sqrt{37}}}{2 \cdot 7} = \frac{{-3 \pm \sqrt{37}}}{14}
\]
The two solutions are:
1. \(x_1 = \frac{{-3 + \sqrt{37}}}{14}\)
2. \(x_2 = \frac{{-3 - \sqrt{37}}}{14}\)
You can use these solutions in the boxes provided:
- Solution 1: \(\frac{{-3 + \sqrt{37}}}{14}\)
- Solution 2: \(\frac{{-3 - \sqrt{37}}}{14}\)
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
where \(a = 7\), \(b = 3\), and \(c = -1\).
First, we calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 3^2 - 4 \cdot 7 \cdot (-1) = 9 + 28 = 37
\]
Since the discriminant is positive, there are two real solutions.
Now, we can substitute the values into the quadratic formula:
\[
x = \frac{{-3 \pm \sqrt{37}}}{2 \cdot 7} = \frac{{-3 \pm \sqrt{37}}}{14}
\]
The two solutions are:
1. \(x_1 = \frac{{-3 + \sqrt{37}}}{14}\)
2. \(x_2 = \frac{{-3 - \sqrt{37}}}{14}\)
You can use these solutions in the boxes provided:
- Solution 1: \(\frac{{-3 + \sqrt{37}}}{14}\)
- Solution 2: \(\frac{{-3 - \sqrt{37}}}{14}\)