Solve x^27x^4 = 3x^4

Question

Solve the equation

x_{1} = - \frac{21}{7}, x_{2} = 0, x_{3} = \frac{21}{7}

Alternative Form

x_{1} \approx - 0.654654, x_{2} = 0, x_{3} \approx 0.654654

Evaluate

x^{2} \times 7 x^{4} = 3 x^{4}

Multiply

More Steps

Evaluate

x^{2} \times 7 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 7

Add the numbers

x^{6} \times 7

Use the commutative property to reorder the terms

7 x^{6}

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

Add or subtract both sides

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

7 x^{2} - 3 = 0

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

7 x^{2} = 0 + 3

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

7 x^{2} = 3

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{3}{7}

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

\frac{3}{7}

Multiply by the Conjugate

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

Multiply the numbers

\frac{21}{7 \times 7}

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

\frac{21}{7}

x = \pm \frac{21}{7}

Separate the equation into 2 possible cases

x = \frac{21}{7} x = - \frac{21}{7}

x = 0 x = \frac{21}{7} x = - \frac{21}{7}

Solution

x_{1} = - \frac{21}{7}, x_{2} = 0, x_{3} = \frac{21}{7}

Alternative Form

x_{1} \approx - 0.654654, x_{2} = 0, x_{3} \approx 0.654654

Show Solution