Question

Solve for x
by factoring
x^2 +4x-21=0
?


Submit

x
=
−
3
x=−3

x
=
−
7
x=−7

x
=
2
x=2

x
=
3
x=3

Answer 1

To solve the quadratic equation \( x^2 + 4x - 21 = 0 \) by factoring, we need to find two numbers that multiply to \(-21\) (the constant term) and add up to \(4\) (the coefficient of the \(x\) term).

The two numbers that satisfy these conditions are \(7\) and \(-3\) because:

- \(7 \times (-3) = -21\)
- \(7 + (-3) = 4\)

Thus, we can factor the quadratic equation as follows:

\[
(x + 7)(x - 3) = 0
\]

Next, we set each factor equal to zero:

1. \(x + 7 = 0 \Rightarrow x = -7\)
2. \(x - 3 = 0 \Rightarrow x = 3\)

So the solutions for \(x\) are:

\[
x = -7 \quad \text{and} \quad x = 3
\]

Hence, the complete solution is:

- \(x = -7\)
- \(x = 3\)

These values can now be identified from your options:
- \(x = -7\)
- \(x = 3\)

(Note that \(x = -3\) and \(x = 2\) are not solutions to the given equation.)