Solve the Quadratic Equation: 3x^2 - 12 = 0

Q: Why do I get two answers for one equation?

Quadratic equations typically have two solutions because when you square a number, both positive and negative values give the same result. For example, both $ 2^2 = 4 $ and $ (-2)^2 = 4 $.

Q: What does the ± symbol mean?

The plus-minus symbol (±) means you have two answers: one with addition and one with subtraction. So $ x = ±2 $ means both $ x = 2 $ and $ x = -2 $.

Q: Can I use the quadratic formula instead?

Yes, but it's unnecessary! When you have $ ax^2 + c = 0 $ (no middle term), the square root method is much faster and simpler than the quadratic formula.

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

If you get something like $ x^2 = -4 $, there are no real solutions because you cannot take the square root of a negative number in basic algebra.

Q: How do I check if both answers are correct?

Substitute each solution back into the original equation separately. Both should make the equation true: $ 3(2)^2 - 12 = 0 $ ✓ and $ 3(-2)^2 - 12 = 0 $ ✓

Quadratic Equations with Square Root Method

Solve the following equation:

$3x^2-12=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Isolate X

00:17 Extract the root

00:24 When extracting a root there are always 2 solutions (positive, negative)

00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$3x^2-12=0$

Step-by-step solution

To solve the equation $3x^2 - 12 = 0$ , follow these steps:

Step 1: Add 12 to both sides to begin isolating $x$ .
Step 2: The equation is now $3x^2 = 12$ .
Step 3: Divide both sides by 3 to solve for $x^2$ , giving us $x^2 = 4$ .
Step 4: Take the square root of both sides, keeping in mind the principle of the plus and minus roots: $x = \pm \sqrt{4}$ .
Step 5: Calculate the square root: $x = \pm 2$ .

Thus, the solutions to the quadratic equation are $x_1 = 2$ and $x_2 = -2$ .

Therefore, the solution to the problem is $x_1 = 2, x_2 = -2$ .

Final Answer

$x_1=6,x_2=-6$

Key Points to Remember

Essential concepts to master this topic

Isolation: Move constant terms to isolate the squared variable first
Technique: Divide by coefficient: $3x^2 = 12$ becomes $x^2 = 4$
Check: Substitute both solutions: $3(2)^2 - 12 = 0$ and $3(-2)^2 - 12 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative square root solution
Don't write just $x = 2$ when solving $x^2 = 4$ = missing half the answer! Square roots have both positive and negative values because both $2^2 = 4$ and $(-2)^2 = 4$ . Always write $x = \pm\sqrt{4} = \pm 2$ .

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

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

FAQ

Everything you need to know about this question

Why do I get two answers for one equation?

Quadratic equations typically have two solutions because when you square a number, both positive and negative values give the same result. For example, both $2^2 = 4$ and $(-2)^2 = 4$ .

What does the ± symbol mean?

The plus-minus symbol (±) means you have two answers: one with addition and one with subtraction. So $x = ±2$ means both $x = 2$ and $x = -2$ .

Can I use the quadratic formula instead?

Yes, but it's unnecessary! When you have $ax^2 + c = 0$ (no middle term), the square root method is much faster and simpler than the quadratic formula.

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

If you get something like $x^2 = -4$ , there are no real solutions because you cannot take the square root of a negative number in basic algebra.

How do I check if both answers are correct?

Substitute each solution back into the original equation separately. Both should make the equation true: $3(2)^2 - 12 = 0$ ✓ and $3(-2)^2 - 12 = 0$ ✓

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Solve the Quadratic Equation: 3x^2 - 12 = 0

Quadratic Equations with Square Root Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I get two answers for one equation?

What does the ± symbol mean?

Can I use the quadratic formula instead?

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

How do I check if both answers are correct?

🌟 Unlock Your Math Potential

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