Solve r^42-201-8000

Question

Simplify the expression

2 r^{4} - 8201

Evaluate

r^{4} \times 2 - 201 - 8000

Use the commutative property to reorder the terms

2 r^{4} - 201 - 8000

Solution

2 r^{4} - 8201

Show Solution

r_{1} = - \frac{4 65608}{2}, r_{2} = \frac{4 65608}{2}

Alternative Form

r_{1} \approx - 8.002196, r_{2} \approx 8.002196

Evaluate

r^{4} \times 2 - 201 - 8000

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

r^{4} \times 2 - 201 - 8000 = 0

Use the commutative property to reorder the terms

2 r^{4} - 201 - 8000 = 0

Subtract the numbers

2 r^{4} - 8201 = 0

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

2 r^{4} = 0 + 8201

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

2 r^{4} = 8201

Divide both sides

\frac{2 r ^{4}}{2} = \frac{8201}{2}

Divide the numbers

r^{4} = \frac{8201}{2}

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

r = \pm 4 \frac{8201}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{8201}{2}

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

\frac{4 8201}{4 2}

Multiply by the Conjugate

\frac{4 8201 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 8201 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

48201 \times 48

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

4 8201 \times 8

Calculate the product

465608

\frac{4 65608}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 65608}{2}

r = \pm \frac{4 65608}{2}

Separate the equation into 2 possible cases

r = \frac{4 65608}{2} r = - \frac{4 65608}{2}

Solution

r_{1} = - \frac{4 65608}{2}, r_{2} = \frac{4 65608}{2}

Alternative Form

r_{1} \approx - 8.002196, r_{2} \approx 8.002196

Show Solution