Solve 4w^24w 1 = 75

Question

Solve the equation

w = \frac{3 300}{4}

Alternative Form

w \approx 1.673582

Evaluate

4 w^{2} \times 4 w \times 1 = 75

Multiply the terms

More Steps

Evaluate

4 w^{2} \times 4 w \times 1

Rewrite the expression

4 w^{2} \times 4 w

Multiply the terms

16 w^{2} \times w

Multiply the terms with the same base by adding their exponents

16 w^{2 + 1}

Add the numbers

16 w^{3}

16 w^{3} = 75

Divide both sides

\frac{16 w ^{3}}{16} = \frac{75}{16}

Divide the numbers

w^{3} = \frac{75}{16}

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

3 w^{3} = 3 \frac{75}{16}

Calculate

w = 3 \frac{75}{16}

Solution

More Steps

Evaluate

3 \frac{75}{16}

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

\frac{3 75}{3 16}

Simplify the radical expression

More Steps

Evaluate

316

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

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

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

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{3 75}{2 3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 75 \times 3 4}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

375 \times 34

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

3 75 \times 4

Calculate the product

3300

\frac{3 300}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 3 2^{2}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{3 300}{4}

w = \frac{3 300}{4}

Alternative Form

w \approx 1.673582

Show Solution