Solve for X: Finding the Value in x·x = 49

Q: Why are there two answers for x?

Because both positive 7 and negative 7 give the same result when multiplied by themselves! Think about it: $ 7 \times 7 = 49 $ and $ (-7) \times (-7) = 49 $ too.

Q: What does the ± symbol mean?

The ± symbol means "plus or minus" - it's a shorthand way to write both solutions at once. So $ x = ±7 $ means x = 7 or x = -7.

Q: Can I solve this without factoring?

Yes! You can also solve by taking the square root of both sides: $ \sqrt{x^2} = \sqrt{49} $, which gives $ x = ±7 $. Both methods work perfectly!

Q: How do I know when to use the difference of squares formula?

Use it when you have two perfect squares subtracted, like $ x^2 - 49 $. The pattern is $ a^2 - b^2 = (a-b)(a+b) $. Here, $ a = x $ and $ b = 7 $.

Q: What if I wrote x = 7 or x = -7 instead of ±7?

That's perfectly correct too! Writing x = 7 or x = -7 shows both solutions clearly. The $ ± $ notation is just a more compact way to write the same thing.

Quadratic Equations with Difference of Squares

Solve for X:

$x\cdot x=49$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the value of X.

00:08 When a number is multiplied by itself, it's called squared.

00:13 Now, let's find the square root of the number.

00:17 Remember, every square root has two answers: one positive and one negative.

00:22 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$x\cdot x=49$

Step-by-step solution

We first rearrange and then set the equations to equal zero.

$x^2-49=0$

$x^2-7^2=0$

We use the abbreviated multiplication formula:

$(x-7)(x+7)=0$

$x=\pm7$

Final Answer

±7

Key Points to Remember

Essential concepts to master this topic

Rule: When $x^2 = k$ , there are two solutions: $x = ±\sqrt{k}$
Technique: Use difference of squares: $x^2 - 49 = (x-7)(x+7) = 0$
Check: Verify both solutions: $7 \cdot 7 = 49$ and $(-7) \cdot (-7) = 49$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution
Don't write just x = 7 when solving $x^2 = 49$ = missing half the answer! Both positive and negative numbers give the same result when squared. Always remember x = ±7 to include both solutions.

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 are there two answers for x?

Because both positive 7 and negative 7 give the same result when multiplied by themselves! Think about it: $7 \times 7 = 49$ and $(-7) \times (-7) = 49$ too.

What does the ± symbol mean?

The ± symbol means "plus or minus" - it's a shorthand way to write both solutions at once. So $x = ±7$ means x = 7 or x = -7.

Can I solve this without factoring?

Yes! You can also solve by taking the square root of both sides: $\sqrt{x^2} = \sqrt{49}$ , which gives $x = ±7$ . Both methods work perfectly!

How do I know when to use the difference of squares formula?

Use it when you have two perfect squares subtracted, like $x^2 - 49$ . The pattern is $a^2 - b^2 = (a-b)(a+b)$ . Here, $a = x$ and $b = 7$ .

What if I wrote x = 7 or x = -7 instead of ±7?

That's perfectly correct too! Writing x = 7 or x = -7 shows both solutions clearly. The $±$ notation is just a more compact way to write the same thing.

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