Solve by completing the square. \[ j^{2}+6 j=49 \] Write your answers as integers, proper or improper fractions in simplest form, or decir rounded to the nearest hundredth.

To solve the equation \( j^{2}+6 j=49 \) by completing the square, we first rearrange the equation: \[ j^{2} + 6j - 49 = 0 \] Next, we focus on the quadratic part, \( j^{2} + 6j \). To complete the square, we take half of the coefficient of \( j \) (which is 6), square it, and add it to both sides: 1. Half of 6 is 3, and \( 3^2 = 9 \). 2. Add 9 to both sides: \[ j^{2} + 6j + 9 = 49 + 9 \] This simplifies to: \[ (j + 3)^{2} = 58 \] Now, to solve for \( j \), we take the square root of both sides: \[ j + 3 = \pm \sqrt{58} \] Subtract 3 from both sides: \[ j = -3 \pm \sqrt{58} \] Thus, the solutions are: \[ j = -3 + \sqrt{58} \quad \text{and} \quad j = -3 - \sqrt{58} \] Approximating \( \sqrt{58} \), which is about 7.62, we get: 1. \( j \approx -3 + 7.62 \approx 4.62 \) 2. \( j \approx -3 - 7.62 \approx -10.62 \) So round your final answer as needed: - \( j \approx 4.62 \) - \( j \approx -10.62 \)