for what values of x is x2 + 2x = 24 true?
–6 and –4 –4 and 6 4 and –6 6 and 4
For what values of x is x2 + 2x = 24 true? –6 and –4 –4 and 6 4 and –6 6 and 4
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for what values of x is x2 + 2x = 24 true?
–6 and –4 –4 and 6 4 and –6 6 and 4
To solve the equation (x^2 + 2x = 24), we first rearrange it into standard form:
[ x^2 + 2x – 24 = 0 ]
Now, we can factor this quadratic equation. We need two numbers that multiply to (-24) and add to (2).
The numbers (6) and (-4) fit these criteria. So we can express the equation as:
[ (x + 6)(x – 4) = 0 ]
Setting each factor to zero gives us the solutions:
1. (x + 6 = 0 implies x = -6)
2. (x – 4 = 0 implies x = 4)
Therefore, the values of (x) that satisfy the equation are (x = -6) and (x = 4).
The correct answer is ( -6 ) and ( 4 ).