Solve the Equation: Combining Like Terms in x² + x² - 3 = x² + 6

Q: Why do I get two answers (±3) instead of just one?

When you solve $ x^2 = 9 $, both positive and negative numbers work! Since $ 3^2 = 9 $ and $ (-3)^2 = 9 $, both x = 3 and x = -3 are correct solutions.

Q: What does 'combining like terms' mean exactly?

Like terms have the same variable and exponent. Here, $ x^2 + x^2 $ becomes $ 2x^2 $ because you're adding two of the same thing, just like 1 apple + 1 apple = 2 apples.

Q: Can I subtract x² from the left side first instead?

It's better to combine like terms first! If you subtract x² from x² + x² without combining, you get a messier equation. Always simplify each side completely before moving terms across.

Q: How do I know which side to move the x² term to?

Move terms to create the simplest equation possible. Since the left side has 2x² and the right has x², subtract x² from both sides to get x² on the left and a number on the right.

Q: What if I forgot the ± sign in my final answer?

You'd only have half the solution! Always remember that $ \sqrt{9} = ±3 $ because both 3² and (-3)² equal 9. Check both values in the original equation to verify.

Quadratic Equations with Like Term Simplification

Solve the following:

$x^2+x^2-3=x^2+6$

❤️ 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 the value of X.

00:09 First, simplify the equation as much as possible.

00:18 Now, let's isolate the variable X.

00:29 Next, we'll extract the root.

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

00:39 And that is the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$x^2+x^2-3=x^2+6$

Step-by-step solution

To solve this problem, we'll follow these steps:

Simplify the given equation.
Solve for $x^2$ and find $x$ .

First, let's simplify the equation:

$x^2 + x^2 - 3 = x^2 + 6$ .

Combine like terms on the left side:

$2x^2 - 3 = x^2 + 6$ .

Subtract $x^2$ from both sides to isolate one of the $x$ terms:

$2x^2 - x^2 - 3 = 6$ .

This simplifies to:

$x^2 - 3 = 6$ .

Next, add 3 to both sides to solve for $x^2$ :

$x^2 = 9$ .

To find $x$ , take the square root of both sides:

$x = \pm\sqrt{9}$ .

This results in:

$x = \pm3$ .

Therefore, the solution to the problem is $\pm3$ .

Final Answer

±3

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine like terms first: x² + x² = 2x²
Technique: Subtract x² from both sides: 2x² - x² = x²
Check: Substitute x = 3: 3² + 3² - 3 = 3² + 6 → 9 = 9 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms on the left side
Don't leave x² + x² uncombined and try to subtract x² from each term separately = confusion and wrong algebra! This makes the problem much harder than it needs to be. Always combine like terms first to get 2x² - 3 = x² + 6, then proceed step by step.

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 (±3) instead of just one?

When you solve $x^2 = 9$ , both positive and negative numbers work! Since $3^2 = 9$ and $(-3)^2 = 9$ , both x = 3 and x = -3 are correct solutions.

What does 'combining like terms' mean exactly?

Like terms have the same variable and exponent. Here, $x^2 + x^2$ becomes $2x^2$ because you're adding two of the same thing, just like 1 apple + 1 apple = 2 apples.

Can I subtract x² from the left side first instead?

It's better to combine like terms first! If you subtract x² from x² + x² without combining, you get a messier equation. Always simplify each side completely before moving terms across.

How do I know which side to move the x² term to?

Move terms to create the simplest equation possible. Since the left side has 2x² and the right has x², subtract x² from both sides to get x² on the left and a number on the right.

What if I forgot the ± sign in my final answer?

You'd only have half the solution! Always remember that $\sqrt{9} = ±3$ because both 3² and (-3)² equal 9. Check both values in the original equation to verify.

🌟 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