Questions: (s+6)(s+3)=-2

Solution Steps

To solve the equation \((s+6)(s+3)=-2\), we need to first expand the left-hand side and then move all terms to one side to form a standard quadratic equation. After that, we can use the quadratic formula to find the values of \(s\).

First, we expand the left-hand side of the equation \((s+6)(s+3) = -2\): \[ (s+6)(s+3) = s^2 + 9s + 18 \]

Next, we move all terms to one side to form a standard quadratic equation: \[ s^2 + 9s + 18 + 2 = 0 \implies s^2 + 9s + 20 = 0 \]

We solve the quadratic equation \(s^2 + 9s + 20 = 0\) using the quadratic formula: \[ s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a = 1\), \(b = 9\), and \(c = 20\).

Calculate the discriminant: \[ \Delta = b^2 - 4ac = 9^2 - 4 \cdot 1 \cdot 20 = 81 - 80 = 1 \]

Using the quadratic formula, we find the roots: \[ s = \frac{-9 \pm \sqrt{1}}{2 \cdot 1} = \frac{-9 \pm 1}{2} \] Thus, the solutions are: \[ s_1 = \frac{-9 + 1}{2} = -4 \quad \text{and} \quad s_2 = \frac{-9 - 1}{2} = -5 \]

Final Answer