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

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Example problems

Type your math problem... x^2 - (k+1)x + k = 0

Question

Solve the equation

Solve for x

Solve for k

x = k x = 1

Evaluate

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

Multiply the terms

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

Rewrite the expression

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

Expand the expression

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

Factor the expression

More Steps

Evaluate

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

Calculate

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

Rewrite the expression

x \times x - x - k x + k

Factor out x from the expression

x (x - 1) - k x + k

Factor out - k from the expression

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

Factor out x - 1 from the expression

(x - k) (x - 1)

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

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

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

Solution

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = k x = 1

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