Question
Solve the equation
Solve for x
Solve for k
x=kx=k+1
Evaluate
x2−(2k+1)x+k2+k=0
Multiply the terms
x2+x(−2k−1)+k2+k=0
Rewrite the expression
x2+(−2k−1)x+k2+k=0
Expand the expression
x2−2kx−x+k2+k=0
Factor the expression
More Steps

Evaluate
x2−2kx−x+k2+k
Calculate
x2−kx−x−kx+k2+k
Rewrite the expression
x×x−xk−x−kx+k×k+k
Factor out x from the expression
x(x−k−1)−kx+k×k+k
Factor out −k from the expression
x(x−k−1)−k(x−k−1)
Factor out x−k−1 from the expression
(x−k)(x−k−1)
(x−k)(x−k−1)=0
When the product of factors equals 0,at least one factor is 0
x−k=0x−k−1=0
Solve the equation for x
More Steps

Evaluate
x−k=0
Move the expression to the right-hand side and change its sign
x=0+k
Add the terms
x=k
x=kx−k−1=0
Solution
More Steps

Evaluate
x−k−1=0
Move the expression to the right-hand side and change its sign
x=0+k+1
Removing 0 doesn't change the value,so remove it from the expression
x=k+1
x=kx=k+1
Show Solution
