15. Solve the equation. There will be more than one correct answer. \( t^{2}-24=0 \) \( t= \)

To solve the equation \( t^{2}-24=0 \), you can start by isolating \( t^{2} \). Adding 24 to both sides gives \( t^{2} = 24 \). Next, take the square root of both sides. Remember, when taking the square root, you have to consider both the positive and negative solutions. Thus, the solutions are: \( t = \sqrt{24} \) or \( t = -\sqrt{24} \). Simplifying further, \( \sqrt{24} \) can be expressed as \( 2\sqrt{6} \). Therefore, the final answers are \( t = 2\sqrt{6} \) and \( t = -2\sqrt{6} \). Fun Fact: This solution represents the concept of roots in mathematics, where every quadratic equation can generally yield two solutions—one positive and one negative! The quadratic formula, which is \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), is a handy shortcut for all quadratic equations, and it always brings us the joys of two possible values. You can apply this in real life, for example, when calculating the height of objects. If you throw a ball straight up, the height at any time can be represented by a quadratic equation similar to this one! Knowing how to solve such equations can help determine how high you can toss that ball before it starts to come back down.