Solve x^2-(2k+1)x+k^2+k=0

Evaluate

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

Multiply the terms

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

Rewrite the expression

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

Expand the expression

x^{2} - 2 k x - x + k^{2} + k = 0

Factor the expression

More Steps

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

When the product of factors equals 0,at least one factor is 0

x - k = 0 x - k - 1 = 0

Solve the equation for x

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x = k x - k - 1 = 0

Solution

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x = k x = k + 1