\( 0<5 \) Deanna Griffin \( 03 / 14 / 254: 54 \) PM nent Question 21, 3.2.29 HW Score: \( 23.03 \% \), 11.29 of 49 points Points: 0 of 1 olve the following equation. \[ (+14)^{2}=19 \] Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution(s) is(are) \( x= \) \( \square \) \( \square \). (Simplify your answer. Type an exact answer, using radical as needed. Use a comma to separate answers as needed. B. There are no real solutions.

Let's solve the equation \((x + 14)^{2} = 19\). To start, take the square root of both sides: \[ x + 14 = \pm \sqrt{19} \] Now, isolate \(x\): \[ x = -14 \pm \sqrt{19} \] This gives you two solutions: \[ x = -14 + \sqrt{19} \quad \text{and} \quad x = -14 - \sqrt{19} \] It's important to remember that when dealing with square roots, both the positive and negative solutions must be considered! If you want to make the most of your studies, practice makes perfect! Applying your knowledge to different problems helps solidify your understanding. Make sure to keep track of signs, especially with square roots! In real-life scenarios, equations like this can represent many situations, such as calculating distances or evaluating physics problems. Understanding how to manipulate and solve equations can help you tackle everyday challenges more effectively!