Solve \(a^2 + (\frac{2a^{2}+a - 1}{2})^2 = 1\)

Evaluate

a^{2} + (\frac{2 a ^{2} + a - 1}{2})^{2} = 1

Move the expression to the left side

a^{2} + (\frac{2 a ^{2} + a - 1}{2})^{2} - 1 = 0

Calculate the sum or difference

More Steps

\frac{1}{4} a^{2} + a^{4} + a^{3} - \frac{1}{2} a - \frac{3}{4} = 0

Factor the expression

\frac{1}{4} (a + 1) (a + 4 a^{3} - 3) = 0

Divide both sides

(a + 1) (a + 4 a^{3} - 3) = 0

Separate the equation into 2 possible cases

a + 1 = 0 a + 4 a^{3} - 3 = 0

Solve the equation

More Steps

a = - 1 a + 4 a^{3} - 3 = 0

Solve the equation

a = - 1 a \approx 0.817183

Solution

a_{1} = - 1, a_{2} \approx 0.817183

Solve the equation