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Solve the equation. (Enter your answers \( a=\square a^{2}-19 a+84=0 \) SUBMIT ANSWER

Ask by Stuart Sherman. in the United States
Feb 21,2025

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\( a=7 \) or \( a=12 \)

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To solve the quadratic equation \( a^2 - 19a + 84 = 0 \), we can factor it. We are looking for two numbers that multiply to 84 and add up to -19. The numbers are -12 and -7. Thus, we can write the equation as: \( (a - 12)(a - 7) = 0 \) Setting each factor to zero gives us the solutions: \( a - 12 = 0 \) or \( a - 7 = 0 \) So, \( a = 12 \) and \( a = 7 \). Final answers: \( a = 12 \) and \( a = 7 \).

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