Solve x^5-7x^4 12x^3

Question

Simplify the expression

x^{5} - 84 x^{7}

Evaluate

x^{5} - 7 x^{4} \times 12 x^{3}

Solution

More Steps

Evaluate

7 x^{4} \times 12 x^{3}

Multiply the terms

84 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

84 x^{4 + 3}

Add the numbers

84 x^{7}

x^{5} - 84 x^{7}

Show Solution

Factor the expression

x^{5} (1 - 84 x^{2})

Evaluate

x^{5} - 7 x^{4} \times 12 x^{3}

Multiply

More Steps

Evaluate

7 x^{4} \times 12 x^{3}

Multiply the terms

84 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

84 x^{4 + 3}

Add the numbers

84 x^{7}

x^{5} - 84 x^{7}

Rewrite the expression

x^{5} - x^{5} \times 84 x^{2}

Solution

x^{5} (1 - 84 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{21}{42}, x_{2} = 0, x_{3} = \frac{21}{42}

Alternative Form

x_{1} \approx - 0.109109, x_{2} = 0, x_{3} \approx 0.109109

Evaluate

x^{5} - 7 x^{4} \times 12 x^{3}

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

x^{5} - 7 x^{4} \times 12 x^{3} = 0

Multiply

More Steps

Multiply the terms

7 x^{4} \times 12 x^{3}

Multiply the terms

84 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

84 x^{4 + 3}

Add the numbers

84 x^{7}

x^{5} - 84 x^{7} = 0

Factor the expression

x^{5} (1 - 84 x^{2}) = 0

Separate the equation into 2 possible cases

x^{5} = 0 1 - 84 x^{2} = 0

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

x = 0 1 - 84 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 84 x^{2} = 0

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

- 84 x^{2} = 0 - 1

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

- 84 x^{2} = - 1

Change the signs on both sides of the equation

84 x^{2} = 1

Divide both sides

\frac{84 x ^{2}}{84} = \frac{1}{84}

Divide the numbers

x^{2} = \frac{1}{84}

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

x = \pm \frac{1}{84}

Simplify the expression

More Steps

Evaluate

\frac{1}{84}

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

\frac{1}{84}

Simplify the radical expression

\frac{1}{84}

Simplify the radical expression

\frac{1}{2 21}

Multiply by the Conjugate

\frac{21}{2 21 \times 21}

Multiply the numbers

\frac{21}{42}

x = \pm \frac{21}{42}

Separate the equation into 2 possible cases

x = \frac{21}{42} x = - \frac{21}{42}

x = 0 x = \frac{21}{42} x = - \frac{21}{42}

Solution

x_{1} = - \frac{21}{42}, x_{2} = 0, x_{3} = \frac{21}{42}

Alternative Form

x_{1} \approx - 0.109109, x_{2} = 0, x_{3} \approx 0.109109

Show Solution