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Use the square root property to solve the equation.(xplus4)squaredequals4Question content area bottomPart 1The solution(s) is/are xequalsenter your response here.(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
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Answered by
GPT-4o mini
To solve the equation \((x + 4)^2 = 4\) using the square root property, we can first take the square root of both sides. The square root property states that if \(a^2 = b\), then \(a = \sqrt{b}\) or \(a = -\sqrt{b}\).
1. Start with the equation:
\[
(x + 4)^2 = 4
\]
2. Apply the square root property:
\[
x + 4 = \sqrt{4} \quad \text{or} \quad x + 4 = -\sqrt{4}
\]
3. Since \(\sqrt{4} = 2\), we have:
\[
x + 4 = 2 \quad \text{or} \quad x + 4 = -2
\]
4. Solve each equation:
- For \(x + 4 = 2\):
\[
x = 2 - 4 \implies x = -2
\]
- For \(x + 4 = -2\):
\[
x = -2 - 4 \implies x = -6
\]
Thus, the solutions are:
\[
x = -2, -6
\]
In conclusion, the solution(s) is/are:
\[
\boxed{-2, -6}
\]
1. Start with the equation:
\[
(x + 4)^2 = 4
\]
2. Apply the square root property:
\[
x + 4 = \sqrt{4} \quad \text{or} \quad x + 4 = -\sqrt{4}
\]
3. Since \(\sqrt{4} = 2\), we have:
\[
x + 4 = 2 \quad \text{or} \quad x + 4 = -2
\]
4. Solve each equation:
- For \(x + 4 = 2\):
\[
x = 2 - 4 \implies x = -2
\]
- For \(x + 4 = -2\):
\[
x = -2 - 4 \implies x = -6
\]
Thus, the solutions are:
\[
x = -2, -6
\]
In conclusion, the solution(s) is/are:
\[
\boxed{-2, -6}
\]
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