Solve 5x^2-15x^68

Question

Simplify the expression

5 x^{2} - 120 x^{6}

Evaluate

5 x^{2} - 15 x^{6} \times 8

Solution

5 x^{2} - 120 x^{6}

Show Solution

5 x^{2} (1 - 24 x^{4})

Evaluate

5 x^{2} - 15 x^{6} \times 8

Multiply the terms

5 x^{2} - 120 x^{6}

Rewrite the expression

5 x^{2} - 5 x^{2} \times 24 x^{4}

Solution

5 x^{2} (1 - 24 x^{4})

Show Solution

x_{1} = - \frac{4 54}{6}, x_{2} = 0, x_{3} = \frac{4 54}{6}

Alternative Form

x_{1} \approx - 0.451801, x_{2} = 0, x_{3} \approx 0.451801

Evaluate

5 x^{2} - 15 x^{6} \times 8

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

5 x^{2} - 15 x^{6} \times 8 = 0

Multiply the terms

5 x^{2} - 120 x^{6} = 0

Factor the expression

5 x^{2} (1 - 24 x^{4}) = 0

Divide both sides

x^{2} (1 - 24 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 24 x^{4} = 0

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

x = 0 1 - 24 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 24 x^{4} = 0

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

- 24 x^{4} = 0 - 1

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

- 24 x^{4} = - 1

Change the signs on both sides of the equation

24 x^{4} = 1

Divide both sides

\frac{24 x ^{4}}{24} = \frac{1}{24}

Divide the numbers

x^{4} = \frac{1}{24}

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

x = \pm 4 \frac{1}{24}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{24}

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

\frac{4 1}{4 24}

Simplify the radical expression

\frac{1}{4 24}

Multiply by the Conjugate

\frac{4 2 4 ^{3}}{4 24 \times 4 2 4 ^{3}}

Simplify

\frac{4 4 54}{4 24 \times 4 2 4 ^{3}}

Multiply the numbers

\frac{4 4 54}{24}

Cancel out the common factor 4

\frac{4 54}{6}

x = \pm \frac{4 54}{6}

Separate the equation into 2 possible cases

x = \frac{4 54}{6} x = - \frac{4 54}{6}

x = 0 x = \frac{4 54}{6} x = - \frac{4 54}{6}

Solution

x_{1} = - \frac{4 54}{6}, x_{2} = 0, x_{3} = \frac{4 54}{6}

Alternative Form

x_{1} \approx - 0.451801, x_{2} = 0, x_{3} \approx 0.451801

Show Solution