Solve 4x^(2)-8x^4=0

Question

Solve the equation

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Evaluate

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

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

x^{2} = 0 1 - 2 x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 2 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 2 x^{2} = 0

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

- 2 x^{2} = 0 - 1

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

- 2 x^{2} = - 1

Change the signs on both sides of the equation

2 x^{2} = 1

Divide both sides

\frac{2 x ^{2}}{2} = \frac{1}{2}

Divide the numbers

x^{2} = \frac{1}{2}

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

x = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

x = \pm \frac{2}{2}

Separate the equation into 2 possible cases

x = \frac{2}{2} x = - \frac{2}{2}

x = 0 x = \frac{2}{2} x = - \frac{2}{2}

Solution

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Show Solution