Question
Three points are plotted on a coordinate plane, forming two intersecting lines.
What is the solution of 2x−7=x2−1
?
(1 point)
The solution to the equation is x=
.
Answers
GPT-4o mini
To solve the equation \(2x - 7 = x^2 - 1\), we start by rearranging it to one side:
\[
x^2 - 2x + 6 = 0
\]
Next, we can apply the quadratic formula, which is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
In our equation, \(a = 1\), \(b = -2\), and \(c = 6\).
1. Calculate the discriminant:
\[
b^2 - 4ac = (-2)^2 - 4(1)(6) = 4 - 24 = -20
\]
Since the discriminant is negative, the equation has no real solutions.
Therefore, there is no real value of \(x\) that satisfies the equation \(2x - 7 = x^2 - 1\).
In conclusion, the solution to the equation is that there are no real solutions.
\[
x^2 - 2x + 6 = 0
\]
Next, we can apply the quadratic formula, which is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
In our equation, \(a = 1\), \(b = -2\), and \(c = 6\).
1. Calculate the discriminant:
\[
b^2 - 4ac = (-2)^2 - 4(1)(6) = 4 - 24 = -20
\]
Since the discriminant is negative, the equation has no real solutions.
Therefore, there is no real value of \(x\) that satisfies the equation \(2x - 7 = x^2 - 1\).
In conclusion, the solution to the equation is that there are no real solutions.