Solve x^(2)-x=\lambda ⋅(2x-1)

Evaluate

x^{2} - x = λ (2 x - 1)

Move the expression to the left side

x^{2} - x - λ (2 x - 1) = 0

Calculate

More Steps

x^{2} - x - 2 λ x + λ = 0

Collect like terms by calculating the sum or difference of their coefficients

x^{2} + (- 1 - 2 λ) x + λ = 0

Substitute a= 1,b= - 1 - 2 λ and c= λ into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 + 2 λ \pm ( - 1 - 2 λ ) ^{2} - 4 λ}{2}

Simplify the expression

More Steps

x = \frac{1 + 2 λ \pm 1 + 4 λ ^{2}}{2}

Solution

x = \frac{1 + 2 λ + 1 + 4 λ ^{2}}{2} x = \frac{1 + 2 λ - 1 + 4 λ ^{2}}{2}

Solve the equation