Solve 7x^(2) 32x-21

Question

Simplify the expression

224 x^{3} - 21

Evaluate

7 x^{2} \times 32 x - 21

Solution

More Steps

Evaluate

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 21

Show Solution

Factor the expression

7 (32 x^{3} - 3)

Evaluate

7 x^{2} \times 32 x - 21

Multiply

More Steps

Evaluate

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 21

Solution

7 (32 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 6}{4}

Alternative Form

x \approx 0.45428

Evaluate

7 x^{2} \times 32 x - 21

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

7 x^{2} \times 32 x - 21 = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 21 = 0

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

224 x^{3} = 0 + 21

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

224 x^{3} = 21

Divide both sides

\frac{224 x ^{3}}{224} = \frac{21}{224}

Divide the numbers

x^{3} = \frac{21}{224}

Cancel out the common factor 7

x^{3} = \frac{3}{32}

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

3 x^{3} = 3 \frac{3}{32}

Calculate

x = 3 \frac{3}{32}

Simplify the root

More Steps

Evaluate

3 \frac{3}{32}

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

\frac{3 3}{3 32}

Simplify the radical expression

More Steps

Evaluate

332

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 4

Write the number in exponential form with the base of 2

3 2^{3} \times 4

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 34

Reduce the index of the radical and exponent with 3

234

\frac{3 3}{2 3 4}

Multiply by the Conjugate

\frac{3 3 \times 3 4 ^{2}}{2 3 4 \times 3 4 ^{2}}

Simplify

\frac{3 3 \times 2 3 2}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 232

Multiply the terms

36 \times 2

Use the commutative property to reorder the terms

236

\frac{2 3 6}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

234 \times 3 4^{2}

Multiply the terms

2 \times 2^{2}

Calculate the product

2^{3}

\frac{2 3 6}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 1}}

Subtract the terms

\frac{1}{2 ^{2}}

\frac{3 6}{2 ^{2}}

x = \frac{3 6}{2 ^{2}}

Solution

x = \frac{3 6}{4}

Alternative Form

x \approx 0.45428

Show Solution