Question

What are the 2 solutions for x^2 - 13x + 42 = 0

Answer 1

To solve the quadratic equation \( x^2 - 13x + 42 = 0 \), we can use the factoring method.

We need to find two numbers that multiply to \( 42 \) (the constant term) and add up to \( -13 \) (the coefficient of \( x \)). The numbers that satisfy these conditions are \( -6 \) and \( -7 \), since:

\[
-6 \times -7 = 42
\]
\[
-6 + -7 = -13
\]

Now, we can factor the equation as:

\[
(x - 6)(x - 7) = 0
\]

Now, we set each factor equal to zero:

1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x - 7 = 0 \) → \( x = 7 \)

Thus, the two solutions for the equation \( x^2 - 13x + 42 = 0 \) are:

\[
x = 6 \quad \text{and} \quad x = 7
\]