Q. \(x^2 – 1 = 0\)
Answer
We solve the equation \(x^2 – 1 = 0\) by adding \(1\) to both sides:
\[x^2 = 1\]
Then take square roots:
\[x = \pm 1\]
Final result: \(x = 1\) or \(x = -1\).
Detailed Explanation
We want to solve the equation
\[
x^2 – 1 = 0
\]
Step 1: Add \(1\) to both sides to isolate the \(x^2\) term.
\[
x^2 – 1 + 1 = 0 + 1
\]
So we get
\[
x^2 = 1
\]
Step 2: Solve \(x^2 = 1\) by taking the square root of both sides.
Recall that if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\). Here \(a = 1\).
\[
x = \pm \sqrt{1}
\]
Step 3: Compute \(\sqrt{1}\).
\[
\sqrt{1} = 1
\]
So
\[
x = \pm 1
\]
Therefore, the solutions are:
\[
x = 1 \quad \text{or} \quad x = -1
\]
See full solution
Graph
Algebra FAQ
Solve \(x^2-1=0\).
Rewrite as \(x^2=1\). Then \(x=\pm1\).
Factor \(x^2-1\).
Use difference of squares: \(x^2-1=(x-1)(x+1)\). Set each factor to zero.
Solve using the quadratic formula.
For \(x^2+0x-1=0\), \(x=\dfrac{-0\pm\sqrt{0^2-4(1)(-1)}}{2(1)}=\pm1\).
What are the roots of \(x^2-1\)?
The roots are \(x=1\) and \(x=-1\), where the expression equals zero.
How to check solutions quickly?
Substitute \(x=1\): \(1^2-1=0\). Substitute \(x=-1\): \((-1)^2-1=0\). Both work.
What is the discriminant of \(x^2-1=0\)?
With \(a=1\), \(b=0\), \(c=-1\), \(\Delta=b^2-4ac=0^2-4(1)(-1)=4\), giving two real roots.
Use these tools to solve it fast!
Check steps for any mistakes!
Check steps for any mistakes!
298,376+ active customers
Math, Geometry, Trigonometry, etc.
Math, Geometry, Trigonometry, etc.
Unlimited AI homework help 
Diagram Generator, Flashcard Maker, Notes Generator, Research Assistant, Answer Generator, AI Homework Helper & AI Detector