Solve 5x^5 - 12x12

Question

Simplify the expression

5 x^{5} - 144 x

Evaluate

5 x^{5} - 12 x \times 12

Solution

5 x^{5} - 144 x

Show Solution

x (5 x^{4} - 144)

Evaluate

5 x^{5} - 12 x \times 12

Multiply the terms

5 x^{5} - 144 x

Rewrite the expression

x \times 5 x^{4} - x \times 144

Solution

x (5 x^{4} - 144)

Show Solution

x_{1} = - \frac{2 4 1125}{5}, x_{2} = 0, x_{3} = \frac{2 4 1125}{5}

Alternative Form

x_{1} \approx - 2.316584, x_{2} = 0, x_{3} \approx 2.316584

Evaluate

5 x^{5} - 12 x \times 12

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

5 x^{5} - 12 x \times 12 = 0

Multiply the terms

5 x^{5} - 144 x = 0

Factor the expression

x (5 x^{4} - 144) = 0

Separate the equation into 2 possible cases

x = 0 5 x^{4} - 144 = 0

Solve the equation

More Steps

Evaluate

5 x^{4} - 144 = 0

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

5 x^{4} = 0 + 144

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

5 x^{4} = 144

Divide both sides

\frac{5 x ^{4}}{5} = \frac{144}{5}

Divide the numbers

x^{4} = \frac{144}{5}

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

x = \pm 4 \frac{144}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{144}{5}

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

\frac{4 144}{4 5}

Simplify the radical expression

\frac{2 3}{4 5}

Multiply by the Conjugate

\frac{2 3 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{2 3 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{2 4 1125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{2 4 1125}{5}

x = \pm \frac{2 4 1125}{5}

Separate the equation into 2 possible cases

x = \frac{2 4 1125}{5} x = - \frac{2 4 1125}{5}

x = 0 x = \frac{2 4 1125}{5} x = - \frac{2 4 1125}{5}

Solution

x_{1} = - \frac{2 4 1125}{5}, x_{2} = 0, x_{3} = \frac{2 4 1125}{5}

Alternative Form

x_{1} \approx - 2.316584, x_{2} = 0, x_{3} \approx 2.316584

Show Solution