Solv e for x. Ent er the solutio ns fro m least to greatest. R cimal place S. (x+3)^2-3=0 lesser x= greater x=

To solve the equation \((x+3)^2 - 3 = 0\), we can follow these steps:<br /><br />1. **Isolate the squared term:**<br /> \[<br /> (x+3)^2 - 3 = 0<br /> \]<br /> Add 3 to both sides:<br /> \[<br /> (x+3)^2 = 3<br /> \]<br /><br />2. **Take the square root of both sides:**<br /> \[<br /> x+3 = \pm \sqrt{3}<br /> \]<br /><br />3. **Solve for \(x\):**<br /> \[<br /> x = -3 + \sqrt{3} \quad \text{or} \quad x = -3 - \sqrt{3}<br /> \]<br /><br />4. **Determine the lesser and greater solutions:**<br /> Since \(\sqrt{3}\) is approximately 1.732, we can approximate the values:<br /> \[<br /> -3 + \sqrt{3} \approx -3 + 1.732 = -1.268<br /> \]<br /> \[<br /> -3 - \sqrt{3} \approx -3 - 1.732 = -4.732<br /> \]<br /><br />Therefore, the solutions from least to greatest are:<br />\[<br />\text{lesser } x = -4.732<br />\]<br />\[<br />\text{greater } x = -1.268<br />\]