\( 1 \leftarrow \quad \) Solve. \( \quad-\sqrt{10 x}+1=-9 \)

Solve the equation \( -\sqrt{10x}+1=-9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-\sqrt{10x}+1=-9\) - step1: Find the domain: \(-\sqrt{10x}+1=-9,x\geq 0\) - step2: Move the constant to the right side: \(-\sqrt{10x}=-9-1\) - step3: Subtract the numbers: \(-\sqrt{10x}=-10\) - step4: Divide both sides: \(\sqrt{10x}=10\) - step5: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{10x}\right)^{2}=10^{2}\) - step6: Evaluate the power: \(10x=100\) - step7: Divide both sides: \(\frac{10x}{10}=\frac{100}{10}\) - step8: Divide the numbers: \(x=10\) - step9: Check if the solution is in the defined range: \(x=10,x\geq 0\) - step10: Find the intersection: \(x=10\) - step11: Check the solution: \(x=10\) The solution to the equation \(-\sqrt{10x}+1=-9\) is \(x=10\).