Solve 6x^6=x^4 - ScanMath

Question

Solve the equation

x_{1} = - \frac{6}{6}, x_{2} = 0, x_{3} = \frac{6}{6}

Alternative Form

x_{1} \approx - 0.408248, x_{2} = 0, x_{3} \approx 0.408248

Evaluate

6 x^{6} = x^{4}

Move the expression to the left side

6 x^{6} - x^{4} = 0

Factor the expression

x^{4} (6 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x^{4} = 0 6 x^{2} - 1 = 0

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

x = 0 6 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

6 x^{2} - 1 = 0

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

6 x^{2} = 0 + 1

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

6 x^{2} = 1

Divide both sides

\frac{6 x ^{2}}{6} = \frac{1}{6}

Divide the numbers

x^{2} = \frac{1}{6}

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

x = \pm \frac{1}{6}

Simplify the expression

More Steps

Evaluate

\frac{1}{6}

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

\frac{1}{6}

Simplify the radical expression

\frac{1}{6}

Multiply by the Conjugate

\frac{6}{6 \times 6}

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

\frac{6}{6}

x = \pm \frac{6}{6}

Separate the equation into 2 possible cases

x = \frac{6}{6} x = - \frac{6}{6}

x = 0 x = \frac{6}{6} x = - \frac{6}{6}

Solution

x_{1} = - \frac{6}{6}, x_{2} = 0, x_{3} = \frac{6}{6}

Alternative Form

x_{1} \approx - 0.408248, x_{2} = 0, x_{3} \approx 0.408248

Show Solution