Solve the equation given by completing the square. 3x^2-12x-15=0 [Hint: Divide by 3 first] x=square

To solve the equation \(3x^2 - 12x - 15 = 0\) by completing the square, follow these steps:<br /><br />1. **Divide the entire equation by 3** to simplify the coefficients:<br /> \[<br /> x^2 - 4x - 5 = 0<br /> \]<br /><br />2. **Move the constant term to the other side** of the equation:<br /> \[<br /> x^2 - 4x = 5<br /> \]<br /><br />3. **Complete the square** on the left side. To do this, take half of the coefficient of \(x\), square it, and add it to both sides of the equation. The coefficient of \(x\) is \(-4\), so half of it is \(-2\), and squaring it gives \(4\):<br /> \[<br /> x^2 - 4x + 4 = 5 + 4<br /> \]<br /> \[<br /> (x - 2)^2 = 9<br /> \]<br /><br />4. **Take the square root of both sides**:<br /> \[<br /> x - 2 = \pm 3<br /> \]<br /><br />5. **Solve for \(x\)** by isolating it:<br /> \[<br /> x = 2 \pm 3<br /> \]<br /><br />So, the solutions are:<br />\[<br />x = 2 + 3 = 5 \quad \text{and} \quad x = 2 - 3 = -1<br />\]<br /><br />Therefore, the solutions to the equation \(3x^2 - 12x - 15 = 0\) are:<br />\[<br />x = 5 \quad \text{and} \quad x = -1<br />\]