To determine whether -2 and 5 are solutions to the quadratic equation \( x^2 + 3x + 2 = 0 \), we can substitute each value into the equation and see if we get a true statement (i.e., whether the left-hand side equals zero).
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Testing x = -2:
Substitute -2 into the equation: \[ (-2)^2 + 3(-2) + 2 \] \[ = 4 - 6 + 2 \] \[ = 4 - 6 + 2 = 0 \]
Since the left-hand side equals 0, \( x = -2 \) is a solution to the equation.
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Testing x = 5:
Substitute 5 into the equation: \[ (5)^2 + 3(5) + 2 \] \[ = 25 + 15 + 2 \] \[ = 25 + 15 + 2 = 42 \]
Since the left-hand side does not equal 0 (it equals 42), \( x = 5 \) is not a solution to the equation.
Conclusion:
- The value -2 is a solution to the equation \( x^2 + 3x + 2 = 0 \), while the value 5 is not a solution.