Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2−2x−11
Evaluate
(x−1)2−12
Expand the expression
x2−2x+1−12
Solution
x2−2x−11
Show Solution
Find the roots
x1=−23+1,x2=23+1
Alternative Form
x1≈−2.464102,x2≈4.464102
Evaluate
(x−1)2−12
To find the roots of the expression,set the expression equal to 0
(x−1)2−12=0
Move the constant to the right-hand side and change its sign
(x−1)2=0+12
Removing 0 doesn't change the value,so remove it from the expression
(x−1)2=12
Take the root of both sides of the equation and remember to use both positive and negative roots
x−1=±12
Simplify the expression
More Steps
Evaluate
12
Write the expression as a product where the root of one of the factors can be evaluated
4×3
Write the number in exponential form with the base of 2
22×3
The root of a product is equal to the product of the roots of each factor
22×3
Reduce the index of the radical and exponent with 2
23
x−1=±23
Separate the equation into 2 possible cases
x−1=23x−1=−23
Move the constant to the right-hand side and change its sign
x=23+1x−1=−23
Move the constant to the right-hand side and change its sign
x=23+1x=−23+1
Solution
x1=−23+1,x2=23+1
Alternative Form
x1≈−2.464102,x2≈4.464102
Show Solution