Question
List the smaller solution first.
x2+4x−5=7
x=
and
x2+4x−5=7
x=
and
Answers
GPT-4o mini
To solve the equation \( x^2 + 4x - 5 = 7 \), we first rearrange it to standard form:
\[
x^2 + 4x - 5 - 7 = 0
\]
\[
x^2 + 4x - 12 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of \(x\)).
The numbers \(6\) and \(-2\) satisfy these conditions:
\[
(x + 6)(x - 2) = 0
\]
Now, we set each factor equal to zero:
1. \(x + 6 = 0\) → \(x = -6\)
2. \(x - 2 = 0\) → \(x = 2\)
Thus, the solutions to the equation \(x^2 + 4x - 5 = 7\) are:
\[
x = -6 \quad \text{and} \quad x = 2
\]
Listing the smaller solution first:
\[
x = -6 \quad \text{and} \quad x = 2
\]
\[
x^2 + 4x - 5 - 7 = 0
\]
\[
x^2 + 4x - 12 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of \(x\)).
The numbers \(6\) and \(-2\) satisfy these conditions:
\[
(x + 6)(x - 2) = 0
\]
Now, we set each factor equal to zero:
1. \(x + 6 = 0\) → \(x = -6\)
2. \(x - 2 = 0\) → \(x = 2\)
Thus, the solutions to the equation \(x^2 + 4x - 5 = 7\) are:
\[
x = -6 \quad \text{and} \quad x = 2
\]
Listing the smaller solution first:
\[
x = -6 \quad \text{and} \quad x = 2
\]