x2+7x+6=0

To solve the quadratic equation \(x^2 + 7x + 6 = 0\), we can factor it.

We want to express the quadratic in the form:

\[ (x + a)(x + b) = 0 \]

where \(a\) and \(b\) are numbers that multiply to \(6\) (the constant term) and add to \(7\) (the coefficient of \(x\)).

Looking for two numbers that satisfy these conditions, we find that \(1\) and \(6\) work because:

• \(1 + 6 = 7\)
• \(1 \times 6 = 6\)

So we can factor the equation as:

\[ (x + 1)(x + 6) = 0 \]

Now, we can set each factor to zero:

1. \(x + 1 = 0 \implies x = -1\)
2. \(x + 6 = 0 \implies x = -6\)

Thus, the solutions to the equation \(x^2 + 7x + 6 = 0\) are:

\[ x = -1 \quad \text{and} \quad x = -6 \]