Solve x^2-2(m-1)*x^2m-5=0

Evaluate

x^{2} - 2 (m - 1) x^{2} m - 5 = 0

Multiply the terms

x^{2} - 2 x^{2} m (m - 1) - 5 = 0

Rewrite the expression

x^{2} + (- 2 m^{2} + 2 m) x^{2} - 5 = 0

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

(1 - 2 m^{2} + 2 m) x^{2} - 5 = 0

Move the constant to the right side

(1 - 2 m^{2} + 2 m) x^{2} = 5

Divide both sides

\frac{( 1 - 2 m ^{2} + 2 m ) x ^{2}}{1 - 2 m ^{2} + 2 m} = \frac{5}{1 - 2 m ^{2} + 2 m}

Divide the numbers

x^{2} = \frac{5}{1 - 2 m ^{2} + 2 m}

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

x = \pm \frac{5}{1 - 2 m ^{2} + 2 m}

Simplify the expression

More Steps

x = \pm \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣}

Separate the equation into 2 possible cases

x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣}

Calculate

{\frac{- 3 + 1}{2} < m < \frac{3 + 1}{2} x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} {\frac{- 3 + 1}{2} < m < \frac{3 + 1}{2} x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} {m > \frac{3 + 1}{2} x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} {m > \frac{3 + 1}{2} x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} {m < \frac{- 3 + 1}{2} x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} {m < \frac{- 3 + 1}{2} x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣}

Solution

\frac{- 3 + 1}{2} < m < \frac{3 + 1}{2}, x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} \frac{- 3 + 1}{2} < m < \frac{3 + 1}{2}, x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} m > \frac{3 + 1}{2}, x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} m > \frac{3 + 1}{2}, x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} m < \frac{- 3 + 1}{2}, x = - \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣} m < \frac{- 3 + 1}{2}, x = \frac{5 - 10 m ^{2} + 10 m}{∣ 1 - 2 m ^{2} + 2 m ∣}

Solve the equation