Solve 4x^216x - 84 = 0

Question

4 x^{2} \times 16 x - 84 = 0

Solve the equation

x = \frac{3 84}{4}

Alternative Form

x \approx 1.09488

Evaluate

4 x^{2} \times 16 x - 84 = 0

Multiply

More Steps

Evaluate

4 x^{2} \times 16 x

Multiply the terms

64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

64 x^{2 + 1}

Add the numbers

64 x^{3}

64 x^{3} - 84 = 0

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

64 x^{3} = 0 + 84

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

64 x^{3} = 84

Divide both sides

\frac{64 x ^{3}}{64} = \frac{84}{64}

Divide the numbers

x^{3} = \frac{84}{64}

Cancel out the common factor 4

x^{3} = \frac{21}{16}

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

3 x^{3} = 3 \frac{21}{16}

Calculate

x = 3 \frac{21}{16}

Solution

More Steps

Evaluate

3 \frac{21}{16}

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

\frac{3 21}{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 21}{2 3 2}

Multiply by the Conjugate

\frac{3 21 \times 3 2 ^{2}}{2 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 21 \times 3 4}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 34

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

3 21 \times 4

Calculate the product

384

\frac{3 84}{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 84}{4}

x = \frac{3 84}{4}

Alternative Form

x \approx 1.09488

Show Solution