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The square root property provides a convenient method to solve certain quadratic equations, especially when they are in the form of a perfect square. It is expressed as: if \((x-a)^2 = b\), then \(x - a = \pm \sqrt{b}\). This means after equating a squared term to a number, you can solve for the unknown variable by taking the square root of the given number, with consideration of both positive and negative roots.

It is important to remember:

• Always apply \(\pm\) because there are typically two possible solutions when working with squared terms.
• The quadratic should be expressed in the form \((x-a)^2\) before applying the property. Sometimes this involves completing the square if it's not already in the desired form.

Understanding this property simplifies the process of solving quadratic equations significantly, as it eliminates the need for complex algebraic manipulations.

A quadratic equation can be intimidating at first glance, but using structured approaches can simplify the solving process. There are several methods to tackle quadratics, including:

• Factoring
• Using the quadratic formula \((-b \pm \sqrt{b^2-4ac})/2a\)
• Graphing
• Completing the square
• Applying the square root property

In the context of our specific problem, where the quadratic is already in the form of a perfect square, applying the square root property is the most straightforward approach. The equation \((x-\frac{5}{2})^2 = 100\) perfectly aligns with this method, allowing quick simplification without expanding the terms.

When you're solving quadratic equations, ensure to correctly handle the square roots and keep your solutions explicit, as demonstrated in our example.

Working through math solutions step-by-step is an effective way to enhance understanding and build confidence in solving problems. Let's recap the steps using the square root property for our equation:

1. **Identify the form**: Check if the quadratic is a perfect square, in our case \((x-\frac{5}{2})^2\).
2. **Apply the square root property**: Set \(x - \frac{5}{2}\) equal to \(\pm \sqrt{100}\), leading to two separate equations to consider.
3. **Solve each equation**:
- First equation: \(x - \frac{5}{2} = 10\), yielding \(x = \frac{25}{2}\) after solving. - Second equation: \(x - \frac{5}{2} = -10\), yielding \(x = -\frac{15}{2}\) after solving.
4. **Double-check**: Verify each solution by substituting back into the original equation to ensure no calculation errors.

Such step-by-step breakdowns demystify problems and show how consistent application of math principles can lead to straightforward solutions, turning complex equations into manageable steps.