Solve x^310x^2-37x^26

Question

Simplify the expression

10 x^{5} - 222 x^{2}

Evaluate

x^{3} \times 10 x^{2} - 37 x^{2} \times 6

Multiply

More Steps

Multiply the terms

x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 10

Add the numbers

x^{5} \times 10

Use the commutative property to reorder the terms

10 x^{5}

10 x^{5} - 37 x^{2} \times 6

Solution

10 x^{5} - 222 x^{2}

Show Solution

Factor the expression

2 x^{2} (5 x^{3} - 111)

Evaluate

x^{3} \times 10 x^{2} - 37 x^{2} \times 6

Multiply

More Steps

Multiply the terms

x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 10

Add the numbers

x^{5} \times 10

Use the commutative property to reorder the terms

10 x^{5}

10 x^{5} - 37 x^{2} \times 6

Multiply the terms

10 x^{5} - 222 x^{2}

Rewrite the expression

2 x^{2} \times 5 x^{3} - 2 x^{2} \times 111

Solution

2 x^{2} (5 x^{3} - 111)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 2775}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 2.810505

Evaluate

x^{3} \times 10 x^{2} - 37 x^{2} \times 6

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

x^{3} \times 10 x^{2} - 37 x^{2} \times 6 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 10

Add the numbers

x^{5} \times 10

Use the commutative property to reorder the terms

10 x^{5}

10 x^{5} - 37 x^{2} \times 6 = 0

Multiply the terms

10 x^{5} - 222 x^{2} = 0

Factor the expression

2 x^{2} (5 x^{3} - 111) = 0

Divide both sides

x^{2} (5 x^{3} - 111) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 x^{3} - 111 = 0

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

x = 0 5 x^{3} - 111 = 0

Solve the equation

More Steps

Evaluate

5 x^{3} - 111 = 0

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

5 x^{3} = 0 + 111

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

5 x^{3} = 111

Divide both sides

\frac{5 x ^{3}}{5} = \frac{111}{5}

Divide the numbers

x^{3} = \frac{111}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{111}{5}

Calculate

x = 3 \frac{111}{5}

Simplify the root

More Steps

Evaluate

3 \frac{111}{5}

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

\frac{3 111}{3 5}

Multiply by the Conjugate

\frac{3 111 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 111 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 2775}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 2775}{5}

x = \frac{3 2775}{5}

x = 0 x = \frac{3 2775}{5}

Solution

x_{1} = 0, x_{2} = \frac{3 2775}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 2.810505

Show Solution