Use a graphing utility to solve the equation. \( e^{x}=-9 x \) The solution set is \( \{\square\} \) (Use a comma to separate answers as needed. Round to two decimal places as needed.)

It seems that there is an issue with solving the equation \(e^{x}=-9x\) using the provided method. Let's try to solve it manually. To solve the equation \(e^{x}=-9x\), we can use the natural logarithm to isolate \(x\). Taking the natural logarithm of both sides of the equation, we get: \[ \ln(e^{x}) = \ln(-9x) \] Using the property of logarithms that \(\ln(e^{x}) = x\), we have: \[ x = \ln(-9x) \] Now, we can solve for \(x\). Let's solve the equation manually. Solve the equation by following steps: - step0: Solve for \(x\): \(x=\ln{\left(-9x\right)}\) - step1: Find the domain: \(x=\ln{\left(-9x\right)},x<0\) - step2: Move the expression to the left side: \(x-\ln{\left(-9x\right)}=0\) - step3: Calculate: \(x\approx -0.100488\) - step4: Check if the solution is in the defined range: \(x\approx -0.100488,x<0\) - step5: Find the intersection: \(x\approx -0.100488\) The solution to the equation \(e^{x}=-9x\) is approximately \(x \approx -0.100488\). Therefore, the solution set is \(\{-0.100488\}\).