Solve x^3 5x^2-17x 11

Question

Simplify the expression

Solution

5 x^{5} - 187 x

Evaluate

x^{3} \times 5 x^{2} - 17 x \times 11

Multiply

More Steps

Multiply the terms

x^{3} \times 5 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 5

Add the numbers

x^{5} \times 5

Use the commutative property to reorder the terms

5 x^{5}

5 x^{5} - 17 x \times 11

Solution

5 x^{5} - 187 x

Show Solution

Factor the expression

Factor

x (5 x^{4} - 187)

Evaluate

x^{3} \times 5 x^{2} - 17 x \times 11

Multiply

More Steps

Multiply the terms

x^{3} \times 5 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 5

Add the numbers

x^{5} \times 5

Use the commutative property to reorder the terms

5 x^{5}

5 x^{5} - 17 x \times 11

Multiply the terms

5 x^{5} - 187 x

Rewrite the expression

x \times 5 x^{4} - x \times 187

Solution

x (5 x^{4} - 187)

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{4 23375}{5}, x_{2} = 0, x_{3} = \frac{4 23375}{5}

Alternative Form

x_{1} \approx - 2.472965, x_{2} = 0, x_{3} \approx 2.472965

Evaluate

x^{3} \times 5 x^{2} - 17 x \times 11

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

x^{3} \times 5 x^{2} - 17 x \times 11 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 5 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 5

Add the numbers

x^{5} \times 5

Use the commutative property to reorder the terms

5 x^{5}

5 x^{5} - 17 x \times 11 = 0

Multiply the terms

5 x^{5} - 187 x = 0

Factor the expression

x (5 x^{4} - 187) = 0

Separate the equation into 2 possible cases

x = 0 5 x^{4} - 187 = 0

Solve the equation

More Steps

Evaluate

5 x^{4} - 187 = 0

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

5 x^{4} = 0 + 187

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

5 x^{4} = 187

Divide both sides

\frac{5 x ^{4}}{5} = \frac{187}{5}

Divide the numbers

x^{4} = \frac{187}{5}

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

x = \pm 4 \frac{187}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{187}{5}

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

\frac{4 187}{4 5}

Multiply by the Conjugate

\frac{4 187 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 187 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 23375}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 23375}{5}

x = \pm \frac{4 23375}{5}

Separate the equation into 2 possible cases

x = \frac{4 23375}{5} x = - \frac{4 23375}{5}

x = 0 x = \frac{4 23375}{5} x = - \frac{4 23375}{5}

Solution

x_{1} = - \frac{4 23375}{5}, x_{2} = 0, x_{3} = \frac{4 23375}{5}

Alternative Form

x_{1} \approx - 2.472965, x_{2} = 0, x_{3} \approx 2.472965

Show Solution

X^3 5x^2 17x 11

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression