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The first step to solving a quadratic equation using the square root property is to isolate the square term. Here, the square term refers to the expression involving the squared variable, which is often of the form \(x^2\). In our problem, we start with the equation \(x^2 - 7 = 0\). To isolate the square term, you need to get \(x^2\) by itself on one side of the equation by performing basic arithmetic operations.

In this specific case, we achieve isolation by adding 7 to both sides of the equation. This eliminates the -7 on the left side:

• Left side: \(x^2 - 7 + 7 = x^2\)
• Right side: \(0 + 7 = 7\)

After carrying out this operation, we have the equation \(x^2 = 7\), which is a crucial step for applying the square root property. Isolating the squared term simplifies the equation and sets it up for further steps.

Quadratic equations like the one we are dealing with can be solved using several methods. One straightforward and useful method is the square root property, especially when the equation can be arranged to have a perfect square term itself. This approach aims to solve for the variable in a single step through isolation and root extraction.

Once we have isolated the square term (\(x^2 = 7\)), we are ready to move to solve it directly by taking its square root. This method is swift because it skips the more elaborate processes of factoring or completing the square. It is an effective strategy when the equation is already, or can easily be written in the form \(x^2 = c\), where \(c\) is a constant number. Remember, our aim is to figure out the value(s) that satisfy the equation.

Having isolated the square term in our quadratic equation, the next step is to take the square root of both sides. The square root property tells us that if \(x^2 = c\), then \(x = \pm\sqrt{c}\). This means we must consider both the positive and negative roots of \(c\), as they are potential solutions.

For our equation \(x^2 = 7\), taking the square root gives:

• \(x = \sqrt{7}\)
• \(x = -\sqrt{7}\)

Therefore, the solutions to this equation are \(x = \sqrt{7}\) and \(x = -\sqrt{7}\). This step highlights the necessity of accounting for the two possible solutions whenever using the square root property. It's crucial because both solutions yield true statements when substituted back into the original equation. This balanced approach ensures that no solutions are overlooked.