Solve 5(x^4)=2x^27

Question

Solve the equation

x_{1} = - \frac{70}{5}, x_{2} = 0, x_{3} = \frac{70}{5}

Alternative Form

x_{1} \approx - 1.67332, x_{2} = 0, x_{3} \approx 1.67332

Evaluate

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

Multiply the terms

5 x^{4} = 14 x^{2}

Add or subtract both sides

5 x^{4} - 14 x^{2} = 0

Factor the expression

x^{2} (5 x^{2} - 14) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 x^{2} - 14 = 0

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

x = 0 5 x^{2} - 14 = 0

Solve the equation

More Steps

Evaluate

5 x^{2} - 14 = 0

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

5 x^{2} = 0 + 14

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

5 x^{2} = 14

Divide both sides

\frac{5 x ^{2}}{5} = \frac{14}{5}

Divide the numbers

x^{2} = \frac{14}{5}

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

x = \pm \frac{14}{5}

Simplify the expression

More Steps

Evaluate

\frac{14}{5}

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

\frac{14}{5}

Multiply by the Conjugate

\frac{14 \times 5}{5 \times 5}

Multiply the numbers

\frac{70}{5 \times 5}

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

\frac{70}{5}

x = \pm \frac{70}{5}

Separate the equation into 2 possible cases

x = \frac{70}{5} x = - \frac{70}{5}

x = 0 x = \frac{70}{5} x = - \frac{70}{5}

Solution

x_{1} = - \frac{70}{5}, x_{2} = 0, x_{3} = \frac{70}{5}

Alternative Form

x_{1} \approx - 1.67332, x_{2} = 0, x_{3} \approx 1.67332

Show Solution