Questions: The solution set of w^2 - 6w = 16 is

Solution Steps

To solve the quadratic equation \( w^2 - 6w = 16 \), we first rearrange it into the standard form \( w^2 - 6w - 16 = 0 \). We can then use the quadratic formula \( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -6 \), and \( c = -16 \), to find the solutions for \( w \).

We start with the equation \( w^2 - 6w = 16 \). Rearranging it into standard form gives us: \[ w^2 - 6w - 16 = 0 \]

Next, we calculate the discriminant \( D \) using the formula \( D = b^2 - 4ac \): \[ D = (-6)^2 - 4 \cdot 1 \cdot (-16) = 36 + 64 = 100 \]

Since the discriminant is positive, we have two real solutions. We apply the quadratic formula: \[ w = \frac{-b \pm \sqrt{D}}{2a} \] Substituting the values: \[ w = \frac{6 \pm \sqrt{100}}{2 \cdot 1} = \frac{6 \pm 10}{2} \] Calculating the two solutions: \[ w_1 = \frac{16}{2} = 8.0 \] \[ w_2 = \frac{-4}{2} = -2.0 \]

Final Answer