Solve 3x^2-19x^6 - ScanMath

Question

Factor the expression

x^{2} (3 - 19 x^{4})

Evaluate

3 x^{2} - 19 x^{6}

Rewrite the expression

x^{2} \times 3 - x^{2} \times 19 x^{4}

Solution

x^{2} (3 - 19 x^{4})

Show Solution

x_{1} = - \frac{4 20577}{19}, x_{2} = 0, x_{3} = \frac{4 20577}{19}

Alternative Form

x_{1} \approx - 0.630365, x_{2} = 0, x_{3} \approx 0.630365

Evaluate

3 x^{2} - 19 x^{6}

To find the roots of the expression,set the expression equal to 0

3 x^{2} - 19 x^{6} = 0

Factor the expression

x^{2} (3 - 19 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 - 19 x^{4} = 0

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

x = 0 3 - 19 x^{4} = 0

Solve the equation

More Steps

Evaluate

3 - 19 x^{4} = 0

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

- 19 x^{4} = 0 - 3

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

- 19 x^{4} = - 3

Change the signs on both sides of the equation

19 x^{4} = 3

Divide both sides

\frac{19 x ^{4}}{19} = \frac{3}{19}

Divide the numbers

x^{4} = \frac{3}{19}

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

x = \pm 4 \frac{3}{19}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{19}

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

\frac{4 3}{4 19}

Multiply by the Conjugate

\frac{4 3 \times 4 1 9 ^{3}}{4 19 \times 4 1 9 ^{3}}

Simplify

\frac{4 3 \times 4 6859}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

\frac{4 20577}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

\frac{4 20577}{19}

x = \pm \frac{4 20577}{19}

Separate the equation into 2 possible cases

x = \frac{4 20577}{19} x = - \frac{4 20577}{19}

x = 0 x = \frac{4 20577}{19} x = - \frac{4 20577}{19}

Solution

x_{1} = - \frac{4 20577}{19}, x_{2} = 0, x_{3} = \frac{4 20577}{19}

Alternative Form

x_{1} \approx - 0.630365, x_{2} = 0, x_{3} \approx 0.630365

Show Solution