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