Rewrite the following equation into a quadratic equation and solve by factoring: x^2+3x=6x+10

Question

. Which of the following contains the correct values for x?(1 point)
Responses

2, −5
2, negative 5

−2
, 5
negative 2 , 5

2, 5
2, 5

−2
, −5

Answer 1

To rewrite the given equation \( x^2 + 3x = 6x + 10 \) into a quadratic equation, we first need to move all terms to one side of the equation:

1. Subtract \( 6x \) and \( 10 \) from both sides: \[ x^2 + 3x - 6x - 10 = 0 \] This simplifies to: \[ x^2 - 3x - 10 = 0 \]

Next, we can factor the quadratic equation \( x^2 - 3x - 10 \). We need to find two numbers that multiply to \(-10\) and add up to \(-3\). The numbers that fit this requirement are \( -5 \) and \( 2 \). Hence, we can factor the quadratic as follows:

\[ (x - 5)(x + 2) = 0 \]

Now we can set each factor equal to zero and solve for \( x \):

1. \( x - 5 = 0 \) gives \( x = 5 \)
2. \( x + 2 = 0 \) gives \( x = -2 \)

So the solutions for \( x \) are:

\[ x = 5 \quad \text{and} \quad x = -2 \]

From the given response options, the correct one that contains the values for \( x \) is:

−2, 5