Solve 10/h^5=7/2 h

Question

Solve the equation

h_{1} = - \frac{6 336140}{7}, h_{2} = \frac{6 336140}{7}

Alternative Form

h_{1} \approx - 1.191211, h_{2} \approx 1.191211

Evaluate

\frac{10}{h ^{5}} = \frac{7}{2} h

Find the domain

More Steps

Evaluate

h^{5} \neq = 0

The only way a power can not be 0 is when the base not equals 0

h \neq = 0

\frac{10}{h ^{5}} = \frac{7}{2} h, h \neq = 0

Rewrite the expression

\frac{10}{h ^{5}} = \frac{7 h}{2}

Cross multiply

10 \times 2 = h^{5} \times 7 h

Simplify the equation

20 = h^{5} \times 7 h

Simplify the equation

20 = 7 h^{6}

Swap the sides of the equation

7 h^{6} = 20

Divide both sides

\frac{7 h ^{6}}{7} = \frac{20}{7}

Divide the numbers

h^{6} = \frac{20}{7}

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

h = \pm 6 \frac{20}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{20}{7}

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

\frac{6 20}{6 7}

Multiply by the Conjugate

\frac{6 20 \times 6 7 ^{5}}{6 7 \times 6 7 ^{5}}

Simplify

\frac{6 20 \times 6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

620 \times 616807

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

6 20 \times 16807

Calculate the product

6336140

\frac{6 336140}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

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

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 336140}{7}

h = \pm \frac{6 336140}{7}

Separate the equation into 2 possible cases

h = \frac{6 336140}{7} h = - \frac{6 336140}{7}

Check if the solution is in the defined range

h = \frac{6 336140}{7} h = - \frac{6 336140}{7}, h \neq = 0

Find the intersection of the solution and the defined range

h = \frac{6 336140}{7} h = - \frac{6 336140}{7}

Solution

h_{1} = - \frac{6 336140}{7}, h_{2} = \frac{6 336140}{7}

Alternative Form

h_{1} \approx - 1.191211, h_{2} \approx 1.191211

Show Solution