Solve x^(4) 5x^(3)-6x^(2)

Question

Simplify the expression

5 x^{7} - 6 x^{2}

Evaluate

x^{4} \times 5 x^{3} - 6 x^{2}

Solution

More Steps

Evaluate

x^{4} \times 5 x^{3}

Multiply the terms with the same base by adding their exponents

x^{4 + 3} \times 5

Add the numbers

x^{7} \times 5

Use the commutative property to reorder the terms

5 x^{7}

5 x^{7} - 6 x^{2}

Show Solution

Factor the expression

x^{2} (5 x^{5} - 6)

Evaluate

x^{4} \times 5 x^{3} - 6 x^{2}

Multiply

More Steps

Evaluate

x^{4} \times 5 x^{3}

Multiply the terms with the same base by adding their exponents

x^{4 + 3} \times 5

Add the numbers

x^{7} \times 5

Use the commutative property to reorder the terms

5 x^{7}

5 x^{7} - 6 x^{2}

Rewrite the expression

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

Solution

x^{2} (5 x^{5} - 6)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 3750}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 1.037137

Evaluate

x^{4} \times 5 x^{3} - 6 x^{2}

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

x^{4} \times 5 x^{3} - 6 x^{2} = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 5 x^{3}

Multiply the terms with the same base by adding their exponents

x^{4 + 3} \times 5

Add the numbers

x^{7} \times 5

Use the commutative property to reorder the terms

5 x^{7}

5 x^{7} - 6 x^{2} = 0

Factor the expression

x^{2} (5 x^{5} - 6) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 x^{5} - 6 = 0

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

x = 0 5 x^{5} - 6 = 0

Solve the equation

More Steps

Evaluate

5 x^{5} - 6 = 0

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

5 x^{5} = 0 + 6

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

5 x^{5} = 6

Divide both sides

\frac{5 x ^{5}}{5} = \frac{6}{5}

Divide the numbers

x^{5} = \frac{6}{5}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{6}{5}

Calculate

x = 5 \frac{6}{5}

Simplify the root

More Steps

Evaluate

5 \frac{6}{5}

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

\frac{5 6}{5 5}

Multiply by the Conjugate

\frac{5 6 \times 5 5 ^{4}}{5 5 \times 5 5 ^{4}}

Simplify

\frac{5 6 \times 5 625}{5 5 \times 5 5 ^{4}}

Multiply the numbers

\frac{5 3750}{5 5 \times 5 5 ^{4}}

Multiply the numbers

\frac{5 3750}{5}

x = \frac{5 3750}{5}

x = 0 x = \frac{5 3750}{5}

Solution

x_{1} = 0, x_{2} = \frac{5 3750}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 1.037137

Show Solution