To solve the equation \( x^2 - 7x - 10 = -2x - 4 \), let's first bring all terms to one side of the equation so that it equals zero.
-
Start by adding \( 2x \) and \( 4 \) to both sides of the equation:
\[ x^2 - 7x - 10 + 2x + 4 = 0 \]
-
Combine like terms:
\[ x^2 - 5x - 6 = 0 \]
Now we can factor the quadratic equation \( x^2 - 5x - 6 \):
-
To factor, we need two numbers that multiply to \(-6\) and add up to \(-5\). These numbers are \(-6\) and \(1\).
\[ (x - 6)(x + 1) = 0 \]
-
Now set each factor equal to zero:
\[ x - 6 = 0 \quad \text{or} \quad x + 1 = 0 \]
-
Solve for \( x \):
\[ x = 6 \quad \text{or} \quad x = -1 \]
Thus, the solutions to the equation are:
\[ x = 6 \quad \text{and} \quad x = -1 \]