Rewrite the following equation into a quadratic equation and solve by factoring: x2+3x=6x+10

Question

Rewrite the following equation into a quadratic equation and solve by factoring: x2+3x=6x+10
. Which of the following contains the correct values for x?(1 point)
Responses

−2
, 5
negative 2 , 5

2, −5
2,  negative 5

2, 5
2, 5

−2
, −5
negative 2 ,  negative 5
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GPT-4o mini · Answer

To rewrite the given equation $ x^2 + 3x = 6x + 10 $, we first bring all terms to one side of the equation: $$ x^2 + 3x - 6x - 10 = 0 $$ Now, we combine like terms: $$ x^2 - 3x - 10 = 0 $$ Next, we factor the quadratic equation $ x^2 - 3x - 10 $. We look for two numbers that multiply to $-10$ and add up to $-3$. The numbers that work are $-5$ and $2$. So, we can factor the equation as follows: $$ (x - 5)(x + 2) = 0 $$ We set each factor equal to zero: 1. $ x - 5 = 0 $ → $ x = 5 $ 2. $ x + 2 = 0 $ → $ x = -2 $ Thus, the solutions to the equation are $ x = 5 $ and $ x = -2 $. The correct response from the options provided is: **−2, 5 (negative 2 , 5)**.