Solve h^4514-21000

Question

Simplify the expression

514 h^{4} - 21000

Evaluate

h^{4} \times 514 - 21000

Solution

514 h^{4} - 21000

Show Solution

2 (257 h^{4} - 10500)

Evaluate

h^{4} \times 514 - 21000

Use the commutative property to reorder the terms

514 h^{4} - 21000

Solution

2 (257 h^{4} - 10500)

Show Solution

h_{1} = - \frac{4 10500 \times 25 7 ^{3}}{257}, h_{2} = \frac{4 10500 \times 25 7 ^{3}}{257}

Alternative Form

h_{1} \approx - 2.528215, h_{2} \approx 2.528215

Evaluate

h^{4} \times 514 - 21000

To find the roots of the expression,set the expression equal to 0

h^{4} \times 514 - 21000 = 0

Use the commutative property to reorder the terms

514 h^{4} - 21000 = 0

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

514 h^{4} = 0 + 21000

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

514 h^{4} = 21000

Divide both sides

\frac{514 h ^{4}}{514} = \frac{21000}{514}

Divide the numbers

h^{4} = \frac{21000}{514}

Cancel out the common factor 2

h^{4} = \frac{10500}{257}

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

h = \pm 4 \frac{10500}{257}

Simplify the expression

More Steps

Evaluate

4 \frac{10500}{257}

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

\frac{4 10500}{4 257}

Multiply by the Conjugate

\frac{4 10500 \times 4 25 7 ^{3}}{4 257 \times 4 25 7 ^{3}}

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

\frac{4 10500 \times 25 7 ^{3}}{4 257 \times 4 25 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

4257 \times 4 25 7^{3}

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

4 257 \times 25 7^{3}

Calculate the product

4 25 7^{4}

Reduce the index of the radical and exponent with 4

257

\frac{4 10500 \times 25 7 ^{3}}{257}

h = \pm \frac{4 10500 \times 25 7 ^{3}}{257}

Separate the equation into 2 possible cases

h = \frac{4 10500 \times 25 7 ^{3}}{257} h = - \frac{4 10500 \times 25 7 ^{3}}{257}

Solution

h_{1} = - \frac{4 10500 \times 25 7 ^{3}}{257}, h_{2} = \frac{4 10500 \times 25 7 ^{3}}{257}

Alternative Form

h_{1} \approx - 2.528215, h_{2} \approx 2.528215

Show Solution