Solve the Quadratic Equation: x² + 9x + 8 = 0

Q: How do I know which two numbers to choose for factoring?

Look for two numbers that multiply to give the constant term (8) and add to give the middle coefficient (9). For this problem: 1 × 8 = 8 and 1 + 8 = 9, so use 1 and 8.

Q: Why are both solutions negative?

When we factor $ x^2 + 9x + 8 = (x + 1)(x + 8) $, setting each factor to zero gives us $ x + 1 = 0 $ and $ x + 8 = 0 $. Solving these gives negative values: x = -1 and x = -8.

Q: Can I use the quadratic formula instead of factoring?

Absolutely! The quadratic formula $ x = \frac{-b ± \sqrt{b^2-4ac}}{2a} $ will give the same answers: x = -1 and x = -8. Factoring is just faster when it's easy to spot the factors.

Q: What if I can't find two numbers that work?

If you can't find factors easily, the quadratic might be unfactorable with integers. In that case, use the quadratic formula or completing the square method instead.

Q: How do I check my factoring is correct?

Expand your factors back out: $ (x + 1)(x + 8) = x^2 + 8x + x + 8 = x^2 + 9x + 8 $. If it matches the original equation, your factoring is correct!

Quadratic Equations with Factoring Method

Solve the following equation:

$x^2+9x+8=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Pay attention to the coefficients

00:10 Use the roots formula

00:21 Substitute appropriate values according to the given data and solve for X

00:39 Calculate the products and the square

00:56 Calculate the square root of 49

01:01 Find the 2 possible solutions

01:10 This is one solution

01:19 This is the second solution and the answer to the question

Step-by-step written solution

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Understand the problem

Solve the following equation:

$x^2+9x+8=0$

Step-by-step solution

To solve the quadratic equation $x^2 + 9x + 8 = 0$ , we will use the factoring method because it appears simple to factor.

First, we attempt to factor the quadratic expression $x^2 + 9x + 8$ . We look for two numbers that multiply to 8 (the constant term) and add up to 9 (the coefficient of the $x$ term).

These numbers are 1 and 8. So, we can write:

$x^2 + 9x + 8 = (x + 1)(x + 8) = 0$

Now, to find the solutions, we set each factor equal to zero:

$x + 1 = 0$ → $x = -1$
$x + 8 = 0$ → $x = -8$

Therefore, the solutions to the equation are $x_1 = -1$ and $x_2 = -8$ .

Upon reviewing the multiple-choice answers, we find that the correct choice is the one that matches our solutions:

$x_1=-1$ $x_2=-8$

Final Answer

$x_1=-1$ $x_2=-8$

Key Points to Remember

Essential concepts to master this topic

Rule: Find two numbers that multiply to constant and add to middle coefficient
Technique: For $x^2 + 9x + 8$ , use 1 and 8 since 1×8=8 and 1+8=9
Check: Substitute both solutions: $(-1)^2 + 9(-1) + 8 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong signs when factoring
Don't write (x - 1)(x - 8) = 0 when you need (x + 1)(x + 8) = 0! This gives positive solutions instead of negative ones. Always check that your factor signs match the original equation's pattern.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

$$ 2x^2-10x-12=0 $$

FAQ

Everything you need to know about this question

How do I know which two numbers to choose for factoring?

Look for two numbers that multiply to give the constant term (8) and add to give the middle coefficient (9). For this problem: 1 × 8 = 8 and 1 + 8 = 9, so use 1 and 8.

Why are both solutions negative?

When we factor $x^2 + 9x + 8 = (x + 1)(x + 8)$ , setting each factor to zero gives us $x + 1 = 0$ and $x + 8 = 0$ . Solving these gives negative values: x = -1 and x = -8.

Can I use the quadratic formula instead of factoring?

Absolutely! The quadratic formula $x = \frac{-b ± \sqrt{b^2-4ac}}{2a}$ will give the same answers: x = -1 and x = -8. Factoring is just faster when it's easy to spot the factors.

What if I can't find two numbers that work?

If you can't find factors easily, the quadratic might be unfactorable with integers. In that case, use the quadratic formula or completing the square method instead.

How do I check my factoring is correct?

Expand your factors back out: $(x + 1)(x + 8) = x^2 + 8x + x + 8 = x^2 + 9x + 8$ . If it matches the original equation, your factoring is correct!

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