To determine if \( x = 4 \) and \( x = 6 \) are solutions to the quadratic equation \( x^2 - 10x + 24 = 0 \), we need to substitute these values into the equation and see if either results in a true statement.
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Testing \( x = 4 \): \[ 4^2 - 10(4) + 24 = 16 - 40 + 24 = 0 \] Since the left side equals 0, \( x = 4 \) is a solution.
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Testing \( x = 6 \): \[ 6^2 - 10(6) + 24 = 36 - 60 + 24 = 0 \] Since the left side also equals 0, \( x = 6 \) is also a solution.
Since both \( x = 4 \) and \( x = 6 \) satisfy the equation, the correct answer is:
Both x = 4 and x = 6 are solutions.