Solve 19x^4 - 5x^2 = 0

Question

Solve the equation

x_{1} = - \frac{95}{19}, x_{2} = 0, x_{3} = \frac{95}{19}

Alternative Form

x_{1} \approx - 0.512989, x_{2} = 0, x_{3} \approx 0.512989

Evaluate

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

Factor the expression

x^{2} (19 x^{2} - 5) = 0

Separate the equation into 2 possible cases

x^{2} = 0 19 x^{2} - 5 = 0

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

x = 0 19 x^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

19 x^{2} - 5 = 0

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

19 x^{2} = 0 + 5

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

19 x^{2} = 5

Divide both sides

\frac{19 x ^{2}}{19} = \frac{5}{19}

Divide the numbers

x^{2} = \frac{5}{19}

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

x = \pm \frac{5}{19}

Simplify the expression

More Steps

Evaluate

\frac{5}{19}

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

\frac{5}{19}

Multiply by the Conjugate

\frac{5 \times 19}{19 \times 19}

Multiply the numbers

\frac{95}{19 \times 19}

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

\frac{95}{19}

x = \pm \frac{95}{19}

Separate the equation into 2 possible cases

x = \frac{95}{19} x = - \frac{95}{19}

x = 0 x = \frac{95}{19} x = - \frac{95}{19}

Solution

x_{1} = - \frac{95}{19}, x_{2} = 0, x_{3} = \frac{95}{19}

Alternative Form

x_{1} \approx - 0.512989, x_{2} = 0, x_{3} \approx 0.512989

Show Solution