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

Question

Solve the equation

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

Evaluate

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

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

x^{2} - \frac{1}{2} = \pm \frac{1}{4}

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

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

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{1}{2}

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

Separate the equation into 2 possible cases

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

Calculate

More Steps

Evaluate

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

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

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

Add the numbers

More Steps

Evaluate

\frac{1}{2} + \frac{1}{2}

Write all numerators above the common denominator

\frac{1 + 1}{2}

Add the numbers

\frac{2}{2}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

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

Calculate

More Steps

Evaluate

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

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

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

Add the numbers

More Steps

Evaluate

- \frac{1}{2} + \frac{1}{2}

Write all numerators above the common denominator

\frac{- 1 + 1}{2}

Add the numbers

\frac{0}{2}

Calculate

0

x^{2} = 0

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

x = 0

x = 1 x = - 1 x = 0

Solution

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

Show Solution