Solve 180 = 2x^545x - 3

Question

Solve the equation

x_{1} = - \frac{6 61 \times 3 0 ^{5}}{30}, x_{2} = \frac{6 61 \times 3 0 ^{5}}{30}

Alternative Form

x_{1} \approx - 1.125559, x_{2} \approx 1.125559

Evaluate

180 = 2 x^{5} \times 45 x - 3

Multiply

More Steps

Evaluate

2 x^{5} \times 45 x

Multiply the terms

90 x^{5} \times x

Multiply the terms with the same base by adding their exponents

90 x^{5 + 1}

Add the numbers

90 x^{6}

180 = 90 x^{6} - 3

Swap the sides of the equation

90 x^{6} - 3 = 180

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

90 x^{6} = 180 + 3

Add the numbers

90 x^{6} = 183

Divide both sides

\frac{90 x ^{6}}{90} = \frac{183}{90}

Divide the numbers

x^{6} = \frac{183}{90}

Cancel out the common factor 3

x^{6} = \frac{61}{30}

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

x = \pm 6 \frac{61}{30}

Simplify the expression

More Steps

Evaluate

6 \frac{61}{30}

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

\frac{6 61}{6 30}

Multiply by the Conjugate

\frac{6 61 \times 6 3 0 ^{5}}{6 30 \times 6 3 0 ^{5}}

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

\frac{6 61 \times 3 0 ^{5}}{6 30 \times 6 3 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

630 \times 6 3 0^{5}

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

6 30 \times 3 0^{5}

Calculate the product

6 3 0^{6}

Reduce the index of the radical and exponent with 6

30

\frac{6 61 \times 3 0 ^{5}}{30}

x = \pm \frac{6 61 \times 3 0 ^{5}}{30}

Separate the equation into 2 possible cases

x = \frac{6 61 \times 3 0 ^{5}}{30} x = - \frac{6 61 \times 3 0 ^{5}}{30}

Solution

x_{1} = - \frac{6 61 \times 3 0 ^{5}}{30}, x_{2} = \frac{6 61 \times 3 0 ^{5}}{30}

Alternative Form

x_{1} \approx - 1.125559, x_{2} \approx 1.125559

Show Solution