Solve for \( y \), where \( y \) is a real number. \[ 1=\sqrt{4 y+16}-1 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Solve the equation \( 1=\sqrt{4y+16}-1 \). Solve the equation by following steps: - step0: Solve for \(y\): \(1=\sqrt{4y+16}-1\) - step1: Find the domain: \(1=\sqrt{4y+16}-1,y\geq -4\) - step2: Simplify the root: \(1=2\sqrt{y+4}-1\) - step3: Swap the sides: \(2\sqrt{y+4}-1=1\) - step4: Move the constant to the right side: \(2\sqrt{y+4}=1-\left(-1\right)\) - step5: Calculate: \(2\sqrt{y+4}=2\) - step6: Divide both sides: \(\sqrt{y+4}=1\) - step7: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{y+4}\right)^{2}=1^{2}\) - step8: Evaluate the power: \(y+4=1\) - step9: Move the constant to the right side: \(y=1-4\) - step10: Subtract the numbers: \(y=-3\) - step11: Check if the solution is in the defined range: \(y=-3,y\geq -4\) - step12: Find the intersection: \(y=-3\) - step13: Check the solution: \(y=-3\) The solution to the equation \(1=\sqrt{4y+16}-1\) is \(y=-3\).