Solve 7x^4 = 3x^6

Question

Solve the equation

x_{1} = - \frac{21}{3}, x_{2} = 0, x_{3} = \frac{21}{3}

Alternative Form

x_{1} \approx - 1.527525, x_{2} = 0, x_{3} \approx 1.527525

Evaluate

7 x^{4} = 3 x^{6}

Add or subtract both sides

7 x^{4} - 3 x^{6} = 0

Factor the expression

x^{4} (7 - 3 x^{2}) = 0

Separate the equation into 2 possible cases

x^{4} = 0 7 - 3 x^{2} = 0

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

x = 0 7 - 3 x^{2} = 0

Solve the equation

More Steps

Evaluate

7 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 7

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

- 3 x^{2} = - 7

Change the signs on both sides of the equation

3 x^{2} = 7

Divide both sides

\frac{3 x ^{2}}{3} = \frac{7}{3}

Divide the numbers

x^{2} = \frac{7}{3}

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

x = \pm \frac{7}{3}

Simplify the expression

More Steps

Evaluate

\frac{7}{3}

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

\frac{7}{3}

Multiply by the Conjugate

\frac{7 \times 3}{3 \times 3}

Multiply the numbers

\frac{21}{3 \times 3}

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

\frac{21}{3}

x = \pm \frac{21}{3}

Separate the equation into 2 possible cases

x = \frac{21}{3} x = - \frac{21}{3}

x = 0 x = \frac{21}{3} x = - \frac{21}{3}

Solution

x_{1} = - \frac{21}{3}, x_{2} = 0, x_{3} = \frac{21}{3}

Alternative Form

x_{1} \approx - 1.527525, x_{2} = 0, x_{3} \approx 1.527525

Show Solution