To solve the equation \(x^2 + 2x = 24\), we first rearrange it to standard quadratic form:
\[ x^2 + 2x - 24 = 0 \]
Next, we can factor the quadratic equation. We need to find two numbers that multiply to \(-24\) (the constant term) and add to \(2\) (the coefficient of the linear term).
The numbers \(6\) and \(-4\) work because:
\[ 6 \times (-4) = -24 \] \[ 6 + (-4) = 2 \]
Thus, we can factor the equation as:
\[ (x + 6)(x - 4) = 0 \]
Setting each factor equal to zero gives us the possible values for \(x\):
- \(x + 6 = 0\) implies \(x = -6\)
- \(x - 4 = 0\) implies \(x = 4\)
Therefore, the solutions to the equation \(x^2 + 2x = 24\) are:
\[ x = -6 \quad \text{and} \quad x = 4 \]
In terms of the answer choices provided, the correct one is:
–6 and 4.
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