Solve x (x-3/2)^2=1/4

Question

Solve the equation

x_{1} = \frac{2 - 3}{2}, x_{2} = 1, x_{3} = \frac{2 + 3}{2}

Alternative Form

x_{1} \approx 0.133975, x_{2} = 1, x_{3} \approx 1.866025

Evaluate

x (x - \frac{3}{2})^{2} = \frac{1}{4}

Expand the expression

More Steps

x^{3} - 3 x^{2} + \frac{9}{4} x = \frac{1}{4}

Move the expression to the left side

x^{3} - 3 x^{2} + \frac{9}{4} x - \frac{1}{4} = 0

Factor the expression

\frac{1}{4} (x - 1) (4 x^{2} - 8 x + 1) = 0

Divide both sides

(x - 1) (4 x^{2} - 8 x + 1) = 0

Separate the equation into 2 possible cases

x - 1 = 0 4 x^{2} - 8 x + 1 = 0

Solve the equation

More Steps

x = 1 4 x^{2} - 8 x + 1 = 0

Solve the equation

More Steps

x = 1 x = \frac{2 + 3}{2} x = \frac{2 - 3}{2}

Solution

x_{1} = \frac{2 - 3}{2}, x_{2} = 1, x_{3} = \frac{2 + 3}{2}

Alternative Form

x_{1} \approx 0.133975, x_{2} = 1, x_{3} \approx 1.866025

Show Solution