1.2 Homework \[ x(x-13)+36=0 \] Selve the following equation by factoring. A. The solution set is \( \{\square\} \). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

To solve the equation by factoring, let's go through the steps systematically. ### Given Equation: \[ x(x - 13) + 36 = 0 \] ### Step 1: Expand the Equation First, expand the left side of the equation: \[ x(x - 13) + 36 = 0 \\ x^2 - 13x + 36 = 0 \] ### Step 2: Factor the Quadratic Equation We need to factor the quadratic equation \( x^2 - 13x + 36 = 0 \). To factor, find two numbers that: - Multiply to **+36** - Add up to **-13** The numbers that satisfy these conditions are **-4** and **-9** because: \[ -4 \times -9 = 36 \\ -4 + (-9) = -13 \] So, the factored form of the equation is: \[ (x - 4)(x - 9) = 0 \] ### Step 3: Solve for \( x \) Set each factor equal to zero and solve for \( x \): \[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \\ x - 9 = 0 \quad \Rightarrow \quad x = 9 \] ### Conclusion The solutions to the equation are \( x = 4 \) and \( x = 9 \). #### A. The solution set is \( \{4, 9\} \). #### B. **Not Applicable**. Since there are valid solutions, statement B ("There is no solution") is **incorrect**.