Solve the Quadratic Equation: x² - 1 = 0

Quadratic Equations with Square Root Method

Solve the following expression:

x2−1=0 x^2-1=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:06 1 squared is always equal to 1
00:10 We'll use the shortened multiplication formulas to find the product
00:16 Let's find what zeros each factor
00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

x2−1=0 x^2-1=0

2

Step-by-step solution

Let's solve the given equation:

x2−1=0 x^2-1=0 We will do this simply by isolating the unknown on one side and taking the square root of both sides:

x2−1=0x2=1/x=±1 x^2-1=0 \\ x^2=1\hspace{6pt}\text{/}\sqrt{\hspace{4pt}}\\ \boxed{x=\pm1}

Therefore, the correct answer is answer A.

3

Final Answer

x=±1 x=\pm1

Key Points to Remember

Essential concepts to master this topic
  • Rule: When x2=a x^2 = a , then x=±a x = \pm\sqrt{a}
  • Technique: Isolate x2 x^2 first: x2−1=0 x^2 - 1 = 0 becomes x2=1 x^2 = 1
  • Check: Substitute both values: (1)2−1=0 (1)^2 - 1 = 0 and (−1)2−1=0 (-1)^2 - 1 = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative solution
    Don't write just x = 1 when solving x2=1 x^2 = 1 = missing half the answer! Since both positive and negative numbers give the same square, you miss the complete solution set. Always write x=±a x = \pm\sqrt{a} when taking square roots.

Practice Quiz

Test your knowledge with interactive questions

\( x^2+6x+9=0 \)

What is the value of X?

FAQ

Everything you need to know about this question

Why does x2=1 x^2 = 1 have two answers?

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Because both positive and negative numbers can have the same square! Since 12=1 1^2 = 1 and (−1)2=1 (-1)^2 = 1 , both values satisfy the original equation.

What does the ± symbol mean?

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The plus-minus symbol (±) is a shorthand way to write two answers at once. x=±1 x = \pm1 means x = 1 OR x = -1.

How do I know when to use the square root method?

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Use this method when you can isolate x2 x^2 by itself on one side. If the equation has an x x term (like x2+3x−4=0 x^2 + 3x - 4 = 0 ), you'll need other methods like factoring or the quadratic formula.

Can I check my answer by plugging it back in?

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Absolutely! For x=1 x = 1 : (1)2−1=1−1=0 (1)^2 - 1 = 1 - 1 = 0 ✓
For x=−1 x = -1 : (−1)2−1=1−1=0 (-1)^2 - 1 = 1 - 1 = 0 ✓

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

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If you end up with something like x2=−4 x^2 = -4 , there are no real solutions because you can't take the square root of a negative number (in basic algebra).

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