Solve 6x^2-13x^6 - ScanMath

Question

Factor the expression

x^{2} (6 - 13 x^{4})

Evaluate

6 x^{2} - 13 x^{6}

Rewrite the expression

x^{2} \times 6 - x^{2} \times 13 x^{4}

Solution

x^{2} (6 - 13 x^{4})

Show Solution

x_{1} = - \frac{4 13182}{13}, x_{2} = 0, x_{3} = \frac{4 13182}{13}

Alternative Form

x_{1} \approx - 0.824237, x_{2} = 0, x_{3} \approx 0.824237

Evaluate

6 x^{2} - 13 x^{6}

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

6 x^{2} - 13 x^{6} = 0

Factor the expression

x^{2} (6 - 13 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 6 - 13 x^{4} = 0

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

x = 0 6 - 13 x^{4} = 0

Solve the equation

More Steps

Evaluate

6 - 13 x^{4} = 0

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

- 13 x^{4} = 0 - 6

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

- 13 x^{4} = - 6

Change the signs on both sides of the equation

13 x^{4} = 6

Divide both sides

\frac{13 x ^{4}}{13} = \frac{6}{13}

Divide the numbers

x^{4} = \frac{6}{13}

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

x = \pm 4 \frac{6}{13}

Simplify the expression

More Steps

Evaluate

4 \frac{6}{13}

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

\frac{4 6}{4 13}

Multiply by the Conjugate

\frac{4 6 \times 4 1 3 ^{3}}{4 13 \times 4 1 3 ^{3}}

Simplify

\frac{4 6 \times 4 2197}{4 13 \times 4 1 3 ^{3}}

Multiply the numbers

\frac{4 13182}{4 13 \times 4 1 3 ^{3}}

Multiply the numbers

\frac{4 13182}{13}

x = \pm \frac{4 13182}{13}

Separate the equation into 2 possible cases

x = \frac{4 13182}{13} x = - \frac{4 13182}{13}

x = 0 x = \frac{4 13182}{13} x = - \frac{4 13182}{13}

Solution

x_{1} = - \frac{4 13182}{13}, x_{2} = 0, x_{3} = \frac{4 13182}{13}

Alternative Form

x_{1} \approx - 0.824237, x_{2} = 0, x_{3} \approx 0.824237

Show Solution