Questions: Solve by applying the zero product property. (m+7)(m-8)=-14

Solution Steps

To solve the equation \((m+7)(m-8) = -14\) using the zero product property, we first need to set the equation to zero by moving -14 to the other side. Then, we can expand the left-hand side and solve the resulting quadratic equation.

To solve \((m+7)(m-8) = -14\) using the zero product property, we first move \(-14\) to the other side of the equation: \[ (m+7)(m-8) + 14 = 0 \]

Next, we expand the left-hand side of the equation: \[ (m+7)(m-8) + 14 = m^2 - 8m + 7m - 56 + 14 = m^2 - m - 42 \] So, the equation becomes: \[ m^2 - m - 42 = 0 \]

We solve the quadratic equation \(m^2 - m - 42 = 0\) using the quadratic formula: \[ m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a = 1\), \(b = -1\), and \(c = -42\). Plugging in these values, we get: \[ m = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \cdot 1 \cdot (-42)}}{2 \cdot 1} = \frac{1 \pm \sqrt{1 + 168}}{2} = \frac{1 \pm \sqrt{169}}{2} = \frac{1 \pm 13}{2} \]

Solving for \(m\), we get two solutions: \[ m = \frac{1 + 13}{2} = 7 \quad \text{and} \quad m = \frac{1 - 13}{2} = -6 \]

Final Answer