Solve $$ x^{2}=-12 x-32 $$ by factoring. a) Rewrite $$ x^{2}=-12 x-32 $$ in factored form. b) The solution set is: $$ \{\square=0 $$ Next Question

Question

Solve $$ x^{2}=-12 x-32 $$ by factoring. a) Rewrite $$ x^{2}=-12 x-32 $$ in factored form. b) The solution set is: $$ \{\square=0 $$ > Next Question

UpStudy AI · Accepted Answer

Sure, let's solve the quadratic equation $$ x^{2} = -12x -32 $$ by factoring step by step.

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### **a) Rewrite $$ x^{2} = -12x -32 $$ in Factored Form**

1. **Bring All Terms to One Side:**

Start by moving all terms to the left side of the equation to set it to zero.

$$
   x^{2} + 12x + 32 = 0
   $$

2. **Factor the Quadratic:**

We need to find two numbers that multiply to **32** (the constant term) and add up to **12** (the coefficient of the middle term).

- The numbers **8** and **4** satisfy this condition because:
     $$
     8 \times 4 = 32 \quad \text{and} \quad 8 + 4 = 12
     $$

3. **Write the Factored Form:**

Using these numbers, the equation can be factored as:

$$
   (x + 8)(x + 4) = 0
   $$

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### **b) The Solution Set**

To find the values of $$ x $$ that satisfy the equation, set each factor equal to zero and solve for $$ x $$.

1. **First Factor:**
   
   $$
   x + 8 = 0 \quad \Rightarrow \quad x = -8
   $$

2. **Second Factor:**
   
   $$
   x + 4 = 0 \quad \Rightarrow \quad x = -4
   $$

3. **Solution Set:**
   
   $$
   \{\, -8,\ -4 \,\}
   $$

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**Final Answer:**

- **a)** The factored form is $$ (x + 8)(x + 4) = 0 $$.
- **b)** The solution set is $$ \{-8,\ -4\} $$.

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> **Next Question**
a) $$ (x + 8)(x + 4) = 0 $$ b) The solution set is $$ \{-8, -4\} $$.

Solve \( x^{2}=-12 x-32 \) by factoring. a) Rewrite \( x^{2}=-12 x-32 \) in factored form. b) The solution set is: \( \{\square=0 \) > Next Question