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The square root property is a powerful tool when solving quadratic equations, especially when they are in the form except of { a=1 } . In our case, the equation is written as . Taking the square root of both sides simplifies the problem significantly. This property works because squaring and taking the square root are inverse operations. In simple terms, whenever you square a number and then take the square root, you return to the original number (considering both positive and negative roots). For instance, . Applying this, introduces a ± symbol to handle both the positive and negative roots. Note: It's essential to handle both cases to ensure we're not missing any solutions.

Isolation of the variable means getting the unknown variable by itself on one side of the equation. We started with the equation . Taking the square root gave us . From here, we need to isolate by getting rid of the that is subtracted on both sides. Add 6 to both sides to obtain : = … If adding or subtracting numbers only on one side, it keeps the equation balanced. This approach of isolating turns the complex equation into much simpler steps. Important note: Always perform the same operation on both sides to maintain equality.

Once we have isolated the variable and solved for , we get two potential values. Remember, the original equation has undergone transformations that may introduce multiple solutions. From and , we find specific solutions and . Combined, they form our final set, represented as . In mathematical terms, the solution set is a collection of all possible values that satisfy the equation. For our example, both and satisfy