Questions: Use factoring to solve the equation x^2-11x+24=0 Rewrite the equation in a completely factored form. =0 (Type your answer in factored form.)

Transcript text: Use factoring to solve the equation $x^{2}-11 x+24=0$ Rewrite the equation in a completely factored form. $\square$ \[ =0 \] (Type your answer in factored form.)

Solution

Solution Steps

Step 1: Write the Equation

We start with the quadratic equation:

\[ x^{2} - 11x + 24 = 0 \]

Step 2: Factor the Quadratic

To factor the quadratic, we need to find two numbers that multiply to $24$ (the constant term) and add up to $-11$ (the coefficient of $x$). The numbers $-8$ and $-3$ satisfy these conditions:

\[ -8 \times -3 = 24 \quad \text{and} \quad -8 + -3 = -11 \]

Thus, we can rewrite the equation in factored form:

\[ (x - 8)(x - 3) = 0 \]

Step 3: Solve for $x$

Setting each factor equal to zero gives us the solutions:

\[ x - 8 = 0 \quad \Rightarrow \quad x = 8 \]

\[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \]