Solve the Quadratic Equation 2x² - 8 = 0: Finding the Roots

Q: What does the ± symbol mean?

The plus-minus symbol (±) means "both positive and negative." So $ x = \pm 2 $ gives us two separate answers: $ x = +2 $ and $ x = -2 $.

Q: Can I use the quadratic formula instead?

Yes, but it's much more work! The quadratic formula works for all quadratic equations, but when you can isolate $ x^2 $ easily like here, taking square roots is faster and simpler.

Q: What if I get a negative number under the square root?

Then the equation has no real solutions! You cannot take the square root of a negative number in real numbers. For example, $ x^2 = -4 $ has no real solutions.

Q: How do I check my answers are correct?

Substitute each solution back into the original equation. For $ x = 2 $: $ 2(2)^2 - 8 = 8 - 8 = 0 $ ✓. For $ x = -2 $: $ 2(-2)^2 - 8 = 8 - 8 = 0 $ ✓.

Quadratic Equations with Square Root Method

Solve the following equation:

$2x^2-8=0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find X together.

00:09 First, we need to isolate X.

00:27 Now, let's extract the root.

00:33 Remember, extracting a root gives us two solutions: one positive and one negative.

00:39 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$2x^2-8=0$

Step-by-step solution

To solve the quadratic equation $2x^2 - 8 = 0$ , we will follow these steps:

Step 1: Isolate $x^2$ .
Step 2: Solve for $x$ by taking square roots.

Let's perform each step:

Step 1: Isolate $x^2$
Start with the given equation:
$2x^2 - 8 = 0$

Add 8 to both sides to isolate the term involving $x$ :
$2x^2 = 8$

Divide both sides by 2 to solve for $x^2$ :
$x^2 = 4$

Step 2: Solve for $x$ by taking square roots
Take the square root of both sides, remembering to consider both the positive and negative roots:
$x = \pm \sqrt{4}$

Simplify the square root:
$x = \pm 2$

This means there are two solutions:
$x_1 = 2$ and $x_2 = -2$

Therefore, the solutions to the equation $2x^2 - 8 = 0$ are $x_1 = -2, x_2 = 2$ .

Matching this with the choices provided, the correct answer is choice 3: $x_1 = -2, x_2 = 2$ .

Final Answer

$x_1=-2,x_2=2$

Key Points to Remember

Essential concepts to master this topic

Rule: Isolate $x^2$ term first before taking square roots
Technique: From $x^2 = 4$ , get $x = \pm 2$ using both roots
Check: Verify both solutions: $2(2)^2 - 8 = 0$ and $2(-2)^2 - 8 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative square root
Don't write just $x = 2$ when solving $x^2 = 4$ = missing half the solutions! Square roots always give both positive and negative values since both $2^2 = 4$ and $(-2)^2 = 4$ . Always write $x = \pm \sqrt{4}$ to get both roots.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$$ 2x^2-8=x^2+4 $$

FAQ

Everything you need to know about this question

Why does the equation have two solutions?

Because when you square both a positive and negative number, you get the same result! Since $2^2 = 4$ and $(-2)^2 = 4$ , both values satisfy $x^2 = 4$ .

What does the ± symbol mean?

The plus-minus symbol (±) means "both positive and negative." So $x = \pm 2$ gives us two separate answers: $x = +2$ and $x = -2$ .

Can I use the quadratic formula instead?

Yes, but it's much more work! The quadratic formula works for all quadratic equations, but when you can isolate $x^2$ easily like here, taking square roots is faster and simpler.

What if I get a negative number under the square root?

Then the equation has no real solutions! You cannot take the square root of a negative number in real numbers. For example, $x^2 = -4$ has no real solutions.

How do I check my answers are correct?

Substitute each solution back into the original equation. For $x = 2$ : $2(2)^2 - 8 = 8 - 8 = 0$ ✓. For $x = -2$ : $2(-2)^2 - 8 = 8 - 8 = 0$ ✓.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Solving Quadratic Equations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime