Factor and solve the quadratic equation: x^2−4x−5=0.

 

Enter the exact answers.

 

The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6
or x+1;x−1). The order of the list does not matter.

To factor and solve the quadratic equation \(x^2 - 4x - 5 = 0\), let's follow these steps:

1. Find two numbers that multiply to give \(-5\) and add to give \(-4\). 
   These numbers are \(-5\) and \(1\), because:
   \[
   (-5) \times 1 = -5 \quad \text{and} \quad (-5) + 1 = -4.
   \]

2. Rewrite the quadratic as:
   \[
   (x - 5)(x + 1) = 0.
   \]

3. Solve for \(x\) by setting each factor equal to zero:
   \[
   x - 5 = 0 \quad \text{or} \quad x + 1 = 0.
   \]
   This gives:
   \[
   x = 5 \quad \text{or} \quad x = -1.
   \]

Thus, the exact solutions are:
\[
x = 5; -1.
\]

Would you like any further details or explanations?

Here are five related questions:
1. How do you verify the solutions of a quadratic equation?
2. What are the other methods to solve a quadratic equation besides factoring?
3. How can the quadratic formula be derived from the standard form of a quadratic equation?
4. What happens if the discriminant of a quadratic equation is negative?
5. Can all quadratic equations be factored?

**Tip:** Always check if factoring is possible by finding two numbers that satisfy the product-sum rule. If not, use the quadratic formula!

Factor and solve the quadratic equation: x^2−4x−5=0.

Learn to factor and solve the quadratic equation x^2 - 4x - 5 = 0 through a step-by-step solution. This problem focuses on algebraic concepts, including factoring techniques and the Zero Product Property, suitable for Grades 8-10.

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