Solve for X: (x+2)² = x² + 12 Perfect Square Equation

Q: Why does the $ x^2 $ term cancel out?

When you expand $ (x+2)^2 = x^2 + 4x + 4 $, you get $ x^2 $ on both sides of the equation. Since they're equal, you can subtract $ x^2 $ from both sides, leaving you with a simpler linear equation!

Q: What's the difference between $ (x+2)^2 $ and $ x^2 + 4 $ ?

$ (x+2)^2 $ expands to three terms: $ x^2 + 4x + 4 $. The middle term $ 4x $ comes from twice the product of the two terms being squared.

Q: How do I remember the perfect square formula?

Think FOIL backwards: First + Outer + Inner + Last becomes $ a^2 + 2ab + b^2 $. The middle term is always twice the product of the two original terms!

Q: Why is the answer x=2 and not x=-2?

After expanding and simplifying, you get $ 4x = 8 $, so $ x = 2 $. Always check your work by substituting back into the original equation to verify!

Perfect Square Expansion with Variable Elimination

Solve for x:

$(x+2)^2=x^2+12$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Use the shortened multiplication formulas to open the parentheses

00:10 Solve the multiplications and squares

00:17 Simplify what we can

00:24 Isolate X

00:38 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 for x:

$(x+2)^2=x^2+12$

Step-by-step solution

Let's solve the equation. First, we'll simplify the algebraic expressions using the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$ We'll then apply the mentioned formula and expand the parentheses in the expression in the equation:

$(x+2)^2=x^2+12 \\ x^2+2\cdot x\cdot2+2^2=x^2+12\\ x^2+4x+4=x^2+12$ We'll continue and combine like terms, by moving terms around. Later - we can notice that the squared term cancels out, therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2+4x+4=x^2+12 \\ 4x=8\hspace{8pt}\text{/}:4\\ \boxed{x=2}$ Therefore, the correct answer is answer C.

Final Answer

$x=2$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $(a+b)^2 = a^2 + 2ab + b^2$ to expand perfectly
Technique: Expand $(x+2)^2 = x^2 + 4x + 4$ then simplify
Check: Substitute x=2: $(2+2)^2 = 16$ and $2^2 + 12 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly expanding the perfect square
Don't expand $(x+2)^2$ as just $x^2 + 4$ = missing the middle term! This forgets the 2ab term and gives wrong answers like x=4 or x=-4. Always remember the complete formula: $(a+b)^2 = a^2 + 2ab + b^2$ .

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that has the same value as the following:

$$ (x+3)^2 $$

FAQ

Everything you need to know about this question

Why does the $x^2$ term cancel out?

When you expand $(x+2)^2 = x^2 + 4x + 4$ , you get $x^2$ on both sides of the equation. Since they're equal, you can subtract $x^2$ from both sides, leaving you with a simpler linear equation!

What's the difference between $(x+2)^2$ and $x^2 + 4$ ?

$(x+2)^2$ expands to three terms: $x^2 + 4x + 4$ . The middle term $4x$ comes from twice the product of the two terms being squared.

How do I remember the perfect square formula?

Think FOIL backwards: First + Outer + Inner + Last becomes $a^2 + 2ab + b^2$ . The middle term is always twice the product of the two original terms!

Can I solve this without expanding first?

You could try taking square roots of both sides, but that gets complicated with the +12. Expanding first is cleaner and shows you exactly what's happening mathematically.

Why is the answer x=2 and not x=-2?

After expanding and simplifying, you get $4x = 8$ , so $x = 2$ . Always check your work by substituting back into the original equation to verify!

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Solve for X: (x+2)² = x² + 12 Perfect Square Equation

Perfect Square Expansion with Variable Elimination

❤️ 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 does the $x^2$ term cancel out?

What's the difference between $(x+2)^2$ and $x^2 + 4$ ?

How do I remember the perfect square formula?

Can I solve this without expanding first?

Why is the answer x=2 and not x=-2?

🌟 Unlock Your Math Potential

More Questions

Square of sum

Solve (x+3)² = x² + 9: Perfect Square Equation Challenge

Solve for X: Finding the Value in (x+3)² = x² + 15

Solve (x-1)² - (x+2)² = 15: Difference of Squared Binomials

Solve the Equation: Finding x in (x+1)² = x² + 13

Solve for X: (x+2)² = x² + 12 Perfect Square Equation

Perfect Square Expansion with Variable Elimination

❤️ 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 does the x2 x^2 x2 term cancel out?

What's the difference between (x+2)2 (x+2)^2 (x+2)2 and x2+4 x^2 + 4 x2+4?

How do I remember the perfect square formula?

Can I solve this without expanding first?

Why is the answer x=2 and not x=-2?

🌟 Unlock Your Math Potential

More Questions

Square of sum

Solve (x+3)² = x² + 9: Perfect Square Equation Challenge

Solve for X: Finding the Value in (x+3)² = x² + 15

Solve (x-1)² - (x+2)² = 15: Difference of Squared Binomials

Solve the Equation: Finding x in (x+1)² = x² + 13

Why does the $x^2$ term cancel out?

What's the difference between $(x+2)^2$ and $x^2 + 4$ ?