9 The area, A, of a rectangular parking lot is given by the equation A=16s^2+25. Jacob knows the area of the parking lot and wants to find s. Solve A=16s^2+25 for s. Enter your answer in the space provided. Enter only your answer.s=□

1. Start with the equation:
   \[A = 16s^ 2 + 25\]
2. Subtract 25 from both sides:
   \[A - 25 = 16s^ 2\]
3. Divide both sides by 16:
   \[\frac { A - 25} { 16} = s^ 2\]
4. Take the square root of both sides:
   \[s = \sqrt { \frac { A - 25} { 16} } \]

Supplemental Knowledge

To solve for \(s\) in the equation \(A = 16s^ 2 + 25\), you need to isolate \(s\). This involves rearranging the equation and using algebraic methods to solve for the variable. Here’s a step-by-step guide:

1. Subtract 25 from both sides of the equation:
   • \(A - 25 = 16s^ 2\)
2. Divide both sides by 16:
   • \(\frac { A - 25} { 16} = s^ 2\)
3. Take the square root of both sides:
   • \(s = \pm \sqrt { \frac { A - 25} { 16} } \)

From Concepts to Reality

Understanding quadratic equations can be essential for real world applications involving physics, engineering and economics. When working on projects requiring optimizing space or materials usage, being able to manipulate and solve quadratic equations effectively will aid you in making accurate calculations and informed decisions.

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