Solve 2x^34x-11=28

Question

Solve the equation

x_{1} = - \frac{4 78}{2}, x_{2} = \frac{4 78}{2}

Alternative Form

x_{1} \approx - 1.485914, x_{2} \approx 1.485914

Evaluate

2 x^{3} \times 4 x - 11 = 28

Multiply

More Steps

Evaluate

2 x^{3} \times 4 x

Multiply the terms

8 x^{3} \times x

Multiply the terms with the same base by adding their exponents

8 x^{3 + 1}

Add the numbers

8 x^{4}

8 x^{4} - 11 = 28

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

8 x^{4} = 28 + 11

Add the numbers

8 x^{4} = 39

Divide both sides

\frac{8 x ^{4}}{8} = \frac{39}{8}

Divide the numbers

x^{4} = \frac{39}{8}

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

x = \pm 4 \frac{39}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{39}{8}

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

\frac{4 39}{4 8}

Multiply by the Conjugate

\frac{4 39 \times 4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{4 39 \times 2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

439 \times 2^{2} 42

Multiply the terms

478 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 478

\frac{2 ^{2} 4 78}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4 8^{3}

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

4 8 \times 8^{3}

Calculate the product

4 8^{4}

Transform the expression

4 2^{12}

Reduce the index of the radical and exponent with 4

2^{3}

\frac{2 ^{2} 4 78}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

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

Simplify

\frac{1}{2}

\frac{4 78}{2}

x = \pm \frac{4 78}{2}

Separate the equation into 2 possible cases

x = \frac{4 78}{2} x = - \frac{4 78}{2}

Solution

x_{1} = - \frac{4 78}{2}, x_{2} = \frac{4 78}{2}

Alternative Form

x_{1} \approx - 1.485914, x_{2} \approx 1.485914

Show Solution