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Solve the given equation by the zero-factor property. \[ x^{2}-36=0 \] The solution set is \( \} \). (Simplify your answer. Type each solution only once. Use a comma to separate ans

Ask by Brooks Mullins. in the United States
Jan 22,2025

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The solution set is \(-6, 6\).

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Beyond the Answer

To solve the equation \( x^{2}-36=0 \) using the zero-factor property, we first rewrite the equation in factored form. Notice that \( 36 \) can be expressed as \( 6^2 \), allowing us to factor the equation as follows: \[ (x - 6)(x + 6) = 0 \] According to the zero-factor property, if a product of factors equals zero, at least one of the factors must equal zero. Thus, we set each factor to zero: 1. \( x - 6 = 0 \) → \( x = 6 \) 2. \( x + 6 = 0 \) → \( x = -6 \) Therefore, the solution set is \( \{ -6, 6 \} \).

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