Solve (x^2)(x^2)(x^2 3x-10)

Question

Simplify the expression

3 x^{7} - 10 x^{4}

Evaluate

x^{2} \times x^{2} (x^{2} \times 3 x - 10)

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

x^{2} \times x^{2} (3 x^{3} - 10)

Multiply the terms with the same base by adding their exponents

x^{2 + 2} (3 x^{3} - 10)

Add the numbers

x^{4} (3 x^{3} - 10)

Apply the distributive property

x^{4} \times 3 x^{3} - x^{4} \times 10

Multiply the terms

More Steps

Evaluate

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{4 + 3}

Add the numbers

x^{7}

3 x^{7}

3 x^{7} - x^{4} \times 10

Solution

3 x^{7} - 10 x^{4}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 90}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 1.493802

Evaluate

(x^{2}) (x^{2}) (x^{2} \times 3 x - 10)

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

(x^{2}) (x^{2}) (x^{2} \times 3 x - 10) = 0

Calculate

x^{2} (x^{2}) (x^{2} \times 3 x - 10) = 0

Calculate

x^{2} \times x^{2} (x^{2} \times 3 x - 10) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

x^{2} \times x^{2} (3 x^{3} - 10) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times x^{2} (3 x^{3} - 10)

Multiply the terms with the same base by adding their exponents

x^{2 + 2} (3 x^{3} - 10)

Add the numbers

x^{4} (3 x^{3} - 10)

x^{4} (3 x^{3} - 10) = 0

Separate the equation into 2 possible cases

x^{4} = 0 3 x^{3} - 10 = 0

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

x = 0 3 x^{3} - 10 = 0

Solve the equation

More Steps

Evaluate

3 x^{3} - 10 = 0

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

3 x^{3} = 0 + 10

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

3 x^{3} = 10

Divide both sides

\frac{3 x ^{3}}{3} = \frac{10}{3}

Divide the numbers

x^{3} = \frac{10}{3}

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

3 x^{3} = 3 \frac{10}{3}

Calculate

x = 3 \frac{10}{3}

Simplify the root

More Steps

Evaluate

3 \frac{10}{3}

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

\frac{3 10}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 10 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 90}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 90}{3}

x = \frac{3 90}{3}

x = 0 x = \frac{3 90}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 90}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 1.493802

Show Solution