To rewrite the equation \(x^2 + 3x = 6x + 10\) into a standard quadratic form, we need to bring all the terms to one side of the equation.
Starting with the given equation:
\[x^2 + 3x - 6x - 10 = 0\]
This simplifies to:
\[x^2 - 3x - 10 = 0\]
Now we have the quadratic equation in standard form. The next step is to factor the equation.
To factor \(x^2 - 3x - 10\), we need two numbers that multiply to -10 (the constant term) and add to -3 (the coefficient of the x term). The numbers that satisfy these conditions are -5 and 2. Thus, we can factor the quadratic as follows:
\[(x - 5)(x + 2) = 0\]
Now, we can set each factor to zero to find the solutions for \(x\):
- \(x - 5 = 0 \implies x = 5\)
- \(x + 2 = 0 \implies x = -2\)
Thus, the solutions to the equation \(x^2 - 3x - 10 = 0\) are:
\[x = 5\] and \[x = -2\]
The correct values for \(x\) are \(-2\) and \(5\).
So the correct answer from the options provided is:
\(-2, 5\) (or "negative 2, 5").