Solve the quadratic equation 84x^2+16x=0 by factoring out the GCF.(1 point) Responses The solutions are x=−421 and x=0 . The solutions are x equals negative Start Fraction 4 over 21 End Fraction and x equals 0 . The solutions are x=0 and x=421 . The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction . The solutions are x=0 and x=4 . The solutions are x equals 0 and x equals 4 . The solutions are x=−4 and x=−421 .

Question

GPT-4o mini · Answer

To solve the quadratic equation $ 84x^2 + 16x = 0 $ by factoring out the greatest common factor (GCF), we first identify the GCF of the terms: 1. $ 84x^2 $ 2. $ 16x $ The GCF of $ 84 $ and $ 16 $ is $ 4 $, and both terms also contain $ x $. Thus, the GCF is $ 4x $. Now, we can factor out $ 4x $ from the equation: $$ 84x^2 + 16x = 4x(21x + 4) = 0 $$ Next, we set each factor equal to zero: 1. From $ 4x = 0 $: $$ x = 0 $$ 2. From $ 21x + 4 = 0 $: $$ 21x = -4 \quad \Rightarrow \quad x = -\frac{4}{21} $$ Thus, the solutions to the equation $ 84x^2 + 16x = 0 $ are: $$ x = 0 \quad \text{and} \quad x = -\frac{4}{21} $$ The correct response is: The solutions are $ x = 0 $ and $ x = -\frac{4}{21} $.