Solve 25x^3 15x^3-9x 1

Question

Simplify the expression

375 x^{6} - 9 x

Evaluate

25 x^{3} \times 15 x^{3} - 9 x \times 1

Multiply

More Steps

Multiply the terms

25 x^{3} \times 15 x^{3}

Multiply the terms

375 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

375 x^{3 + 3}

Add the numbers

375 x^{6}

375 x^{6} - 9 x \times 1

Solution

375 x^{6} - 9 x

Show Solution

Factor the expression

3 x (125 x^{5} - 3)

Evaluate

25 x^{3} \times 15 x^{3} - 9 x \times 1

Multiply

More Steps

Multiply the terms

25 x^{3} \times 15 x^{3}

Multiply the terms

375 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

375 x^{3 + 3}

Add the numbers

375 x^{6}

375 x^{6} - 9 x \times 1

Multiply the terms

375 x^{6} - 9 x

Rewrite the expression

3 x \times 125 x^{5} - 3 x \times 3

Solution

3 x (125 x^{5} - 3)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 75}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.474288

Evaluate

25 x^{3} \times 15 x^{3} - 9 x \times 1

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

25 x^{3} \times 15 x^{3} - 9 x \times 1 = 0

Multiply

More Steps

Multiply the terms

25 x^{3} \times 15 x^{3}

Multiply the terms

375 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

375 x^{3 + 3}

Add the numbers

375 x^{6}

375 x^{6} - 9 x \times 1 = 0

Multiply the terms

375 x^{6} - 9 x = 0

Factor the expression

3 x (125 x^{5} - 3) = 0

Divide both sides

x (125 x^{5} - 3) = 0

Separate the equation into 2 possible cases

x = 0 125 x^{5} - 3 = 0

Solve the equation

More Steps

Evaluate

125 x^{5} - 3 = 0

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

125 x^{5} = 0 + 3

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

125 x^{5} = 3

Divide both sides

\frac{125 x ^{5}}{125} = \frac{3}{125}

Divide the numbers

x^{5} = \frac{3}{125}

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

5 x^{5} = 5 \frac{3}{125}

Calculate

x = 5 \frac{3}{125}

Simplify the root

More Steps

Evaluate

5 \frac{3}{125}

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

\frac{5 3}{5 125}

Multiply by the Conjugate

\frac{5 3 \times 5 12 5 ^{4}}{5 125 \times 5 12 5 ^{4}}

Simplify

\frac{5 3 \times 5 ^{2} 5 25}{5 125 \times 5 12 5 ^{4}}

Multiply the numbers

\frac{5 ^{2} 5 75}{5 125 \times 5 12 5 ^{4}}

Multiply the numbers

\frac{5 ^{2} 5 75}{5 ^{3}}

Reduce the fraction

\frac{5 75}{5}

x = \frac{5 75}{5}

x = 0 x = \frac{5 75}{5}

Solution

x_{1} = 0, x_{2} = \frac{5 75}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.474288

Show Solution