Solve 180 = 2x^54x 19

Question

Solve the equation

x_{1} = - \frac{6 45 \times 3 8 ^{5}}{38}, x_{2} = \frac{6 45 \times 3 8 ^{5}}{38}

Alternative Form

x_{1} \approx - 1.02858, x_{2} \approx 1.02858

Evaluate

180 = 2 x^{5} \times 4 x \times 19

Multiply

More Steps

Evaluate

2 x^{5} \times 4 x \times 19

Multiply the terms

More Steps

Evaluate

2 \times 4 \times 19

Multiply the terms

8 \times 19

Multiply the numbers

152

152 x^{5} \times x

Multiply the terms with the same base by adding their exponents

152 x^{5 + 1}

Add the numbers

152 x^{6}

180 = 152 x^{6}

Swap the sides of the equation

152 x^{6} = 180

Divide both sides

\frac{152 x ^{6}}{152} = \frac{180}{152}

Divide the numbers

x^{6} = \frac{180}{152}

Cancel out the common factor 4

x^{6} = \frac{45}{38}

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

x = \pm 6 \frac{45}{38}

Simplify the expression

More Steps

Evaluate

6 \frac{45}{38}

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

\frac{6 45}{6 38}

Multiply by the Conjugate

\frac{6 45 \times 6 3 8 ^{5}}{6 38 \times 6 3 8 ^{5}}

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

\frac{6 45 \times 3 8 ^{5}}{6 38 \times 6 3 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

638 \times 6 3 8^{5}

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

6 38 \times 3 8^{5}

Calculate the product

6 3 8^{6}

Reduce the index of the radical and exponent with 6

38

\frac{6 45 \times 3 8 ^{5}}{38}

x = \pm \frac{6 45 \times 3 8 ^{5}}{38}

Separate the equation into 2 possible cases

x = \frac{6 45 \times 3 8 ^{5}}{38} x = - \frac{6 45 \times 3 8 ^{5}}{38}

Solution

x_{1} = - \frac{6 45 \times 3 8 ^{5}}{38}, x_{2} = \frac{6 45 \times 3 8 ^{5}}{38}

Alternative Form

x_{1} \approx - 1.02858, x_{2} \approx 1.02858

Show Solution