Solve (x-1)⋅(x-1)-1

Question

Simplify the expression

x^{2} - 2 x

Evaluate

(x - 1) (x - 1) - 1

Multiply the terms

(x - 1)^{2} - 1

Expand the expression

x^{2} - 2 x + 1 - 1

Solution

x^{2} - 2 x

Show Solution

(x - 2) x

Evaluate

(x - 1) (x - 1) - 1

Evaluate

(x - 1)^{2} - 1

Rewrite the expression in exponential form

(x - 1)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x - 1 - 1) (x - 1 + 1)

Evaluate

(x - 2) (x - 1 + 1)

Solution

(x - 2) x

Show Solution

x_{1} = 0, x_{2} = 2

Evaluate

(x - 1) (x - 1) - 1

To find the roots of the expression,set the expression equal to 0

(x - 1) (x - 1) - 1 = 0

Multiply the terms

(x - 1)^{2} - 1 = 0

Move the constant to the right-hand side and change its sign

(x - 1)^{2} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

(x - 1)^{2} = 1

Take the root of both sides of the equation and remember to use both positive and negative roots

x - 1 = \pm 1

Simplify the expression

x - 1 = \pm 1

Separate the equation into 2 possible cases

x - 1 = 1 x - 1 = - 1

Calculate

More Steps

Evaluate

x - 1 = 1

Move the constant to the right-hand side and change its sign

x = 1 + 1

Add the numbers

x = 2

x = 2 x - 1 = - 1

Calculate

More Steps

Evaluate

x - 1 = - 1

Move the constant to the right-hand side and change its sign

x = - 1 + 1

Add the numbers

x = 0

x = 2 x = 0

Solution

x_{1} = 0, x_{2} = 2

Show Solution