Solve 10x^322x^2-24x

Question

Simplify the expression

220 x^{5} - 24 x

Evaluate

10 x^{3} \times 22 x^{2} - 24 x

Solution

More Steps

Evaluate

10 x^{3} \times 22 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

220 x^{3 + 2}

Add the numbers

220 x^{5}

220 x^{5} - 24 x

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Factor the expression

4 x (55 x^{4} - 6)

Evaluate

10 x^{3} \times 22 x^{2} - 24 x

Multiply

More Steps

Evaluate

10 x^{3} \times 22 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

220 x^{3 + 2}

Add the numbers

220 x^{5}

220 x^{5} - 24 x

Rewrite the expression

4 x \times 55 x^{4} - 4 x \times 6

Solution

4 x (55 x^{4} - 6)

Show Solution

Find the roots

x_{1} = - \frac{4 6 \times 5 5 ^{3}}{55}, x_{2} = 0, x_{3} = \frac{4 6 \times 5 5 ^{3}}{55}

Alternative Form

x_{1} \approx - 0.574708, x_{2} = 0, x_{3} \approx 0.574708

Evaluate

10 x^{3} \times 22 x^{2} - 24 x

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

10 x^{3} \times 22 x^{2} - 24 x = 0

Multiply

More Steps

Multiply the terms

10 x^{3} \times 22 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

220 x^{3 + 2}

Add the numbers

220 x^{5}

220 x^{5} - 24 x = 0

Factor the expression

4 x (55 x^{4} - 6) = 0

Divide both sides

x (55 x^{4} - 6) = 0

Separate the equation into 2 possible cases

x = 0 55 x^{4} - 6 = 0

Solve the equation

More Steps

Evaluate

55 x^{4} - 6 = 0

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

55 x^{4} = 0 + 6

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

55 x^{4} = 6

Divide both sides

\frac{55 x ^{4}}{55} = \frac{6}{55}

Divide the numbers

x^{4} = \frac{6}{55}

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

x = \pm 4 \frac{6}{55}

Simplify the expression

More Steps

Evaluate

4 \frac{6}{55}

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

\frac{4 6}{4 55}

Multiply by the Conjugate

\frac{4 6 \times 4 5 5 ^{3}}{4 55 \times 4 5 5 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 6 \times 5 5 ^{3}}{4 55 \times 4 5 5 ^{3}}

Multiply the numbers

\frac{4 6 \times 5 5 ^{3}}{55}

x = \pm \frac{4 6 \times 5 5 ^{3}}{55}

Separate the equation into 2 possible cases

x = \frac{4 6 \times 5 5 ^{3}}{55} x = - \frac{4 6 \times 5 5 ^{3}}{55}

x = 0 x = \frac{4 6 \times 5 5 ^{3}}{55} x = - \frac{4 6 \times 5 5 ^{3}}{55}

Solution

x_{1} = - \frac{4 6 \times 5 5 ^{3}}{55}, x_{2} = 0, x_{3} = \frac{4 6 \times 5 5 ^{3}}{55}

Alternative Form

x_{1} \approx - 0.574708, x_{2} = 0, x_{3} \approx 0.574708

Show Solution