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 , negative 5

2, −5
2, negative 5

2, 5
2, 5

−2
, 5
negative 2 , 5
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Answer 1

To rewrite the equation \( x^2 + 3x = 6x + 10 \) into standard quadratic form, we start by moving all terms to one side of the equation:

\[
x^2 + 3x - 6x - 10 = 0
\]

Combining like terms gives:

\[
x^2 - 3x - 10 = 0
\]

Next, we will factor the quadratic equation. We are looking for two numbers that multiply to \(-10\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)). The numbers \(-5\) and \(2\) work since:

\[
-5 \times 2 = -10 \quad \text{and} \quad -5 + 2 = -3
\]

This allows us to factor the quadratic as follows:

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

To find the solutions, we set each factor equal to zero:

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

Therefore, the solutions to the quadratic equation are:

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

The correct response reflecting the values for \(x\) is:

**−2, 5** (negative 2, 5).