Solve the Quadratic Equation: x² = 10 and Explore Its Roots

Quadratic Equations with Perfect Square Simplification

Resolve:

0=x2−100 0=x^2-\sqrt{100}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve the problem step by step.
00:08 First, calculate the square root of one hundred.
00:12 Next, isolate the variable X.
00:23 Now, extract the root to find the solution.
00:31 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Resolve:

0=x2−100 0=x^2-\sqrt{100}

2

Step-by-step solution

To resolve the equation 0=x2−1000 = x^2 - \sqrt{100}, follow these steps:

  • Simplify 100\sqrt{100}:
    100=10\sqrt{100} = 10 as 100 is a perfect square.
  • Rewrite the equation using the simplified term:
    x2=10x^2 = 10.
  • Apply the square root property to solve for xx:
    x=±10x = \pm\sqrt{10}.

Therefore, the solution to the equation is x=±10 x = \pm\sqrt{10} .

3

Final Answer

±10 \pm\sqrt{10}

Key Points to Remember

Essential concepts to master this topic
  • Perfect Squares: 100=10 \sqrt{100} = 10 because 102=100 10^2 = 100
  • Square Root Property: If x2=10 x^2 = 10 , then x=±10 x = \pm\sqrt{10}
  • Check: Substitute both solutions: (±10)2=10 (\pm\sqrt{10})^2 = 10 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative solution
    Don't write just x=10 x = \sqrt{10} = missing half the answer! When you square both positive and negative numbers, you get the same result. Always include the ± symbol for 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 do I need both positive and negative solutions?

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Because when you square any number, positive or negative, the result is positive! Both (10)2=10 (\sqrt{10})^2 = 10 and (−10)2=10 (-\sqrt{10})^2 = 10 work.

How do I simplify 100 \sqrt{100} ?

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Ask yourself: "What number times itself equals 100?" Since 10×10=100 10 \times 10 = 100 , we have 100=10 \sqrt{100} = 10 .

What if the number under the square root isn't a perfect square?

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Then you leave it as a radical! For example, if x2=7 x^2 = 7 , the answer is x=±7 x = \pm\sqrt{7} since 7 isn't a perfect square.

Can I write ±10 \pm10 instead of ±10 \pm\sqrt{10} ?

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No! That would mean x=10 x = 10 or x=−10 x = -10 . But 102=100 10^2 = 100 , not 10. Always check: does your answer squared equal the original number?

How do I check my work?

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Substitute both solutions back into the original equation. For x=10 x = \sqrt{10} : (10)2−10=10−10=0 (\sqrt{10})^2 - 10 = 10 - 10 = 0 ✓

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