3. Solve \( h(h-3)=5 h+18 \). Correct your answer to 3 significant figures.

To solve the equation \( h(h-3)=5h+18 \), we start by expanding the left side: \[ h^2 - 3h = 5h + 18 \] Rearranging the equation gives us: \[ h^2 - 3h - 5h - 18 = 0 \] This simplifies to: \[ h^2 - 8h - 18 = 0 \] Next, we can use the quadratic formula \( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -8 \), and \( c = -18 \). Calculating the discriminant: \[ b^2 - 4ac = (-8)^2 - 4(1)(-18) = 64 + 72 = 136 \] Now, applying the quadratic formula: \[ h = \frac{-(-8) \pm \sqrt{136}}{2(1)} = \frac{8 \pm \sqrt{136}}{2} \] Calculating \( \sqrt{136} \) gives \( \sqrt{136} \approx 11.664 \). Thus, we have: \[ h = \frac{8 \pm 11.664}{2} \] This results in two potential solutions: 1. \( h = \frac{8 + 11.664}{2} \approx \frac{19.664}{2} \approx 9.832 \) 2. \( h = \frac{8 - 11.664}{2} \approx \frac{-3.664}{2} \approx -1.832 \) Now correcting to three significant figures, we obtain: - \( h \approx 9.83 \) - \( h \approx -1.83 \) Therefore, the solutions rounded to three significant figures are \( h \approx 9.83 \) and \( h \approx -1.83 \).