Solve d^4340-60004

Question

Simplify the expression

340 d^{4} - 60004

Evaluate

d^{4} \times 340 - 60004

Solution

340 d^{4} - 60004

Show Solution

4 (85 d^{4} - 15001)

Evaluate

d^{4} \times 340 - 60004

Use the commutative property to reorder the terms

340 d^{4} - 60004

Solution

4 (85 d^{4} - 15001)

Show Solution

d_{1} = - \frac{4 15001 \times 8 5 ^{3}}{85}, d_{2} = \frac{4 15001 \times 8 5 ^{3}}{85}

Alternative Form

d_{1} \approx - 3.644814, d_{2} \approx 3.644814

Evaluate

d^{4} \times 340 - 60004

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

d^{4} \times 340 - 60004 = 0

Use the commutative property to reorder the terms

340 d^{4} - 60004 = 0

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

340 d^{4} = 0 + 60004

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

340 d^{4} = 60004

Divide both sides

\frac{340 d ^{4}}{340} = \frac{60004}{340}

Divide the numbers

d^{4} = \frac{60004}{340}

Cancel out the common factor 4

d^{4} = \frac{15001}{85}

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

d = \pm 4 \frac{15001}{85}

Simplify the expression

More Steps

Evaluate

4 \frac{15001}{85}

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

\frac{4 15001}{4 85}

Multiply by the Conjugate

\frac{4 15001 \times 4 8 5 ^{3}}{4 85 \times 4 8 5 ^{3}}

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

\frac{4 15001 \times 8 5 ^{3}}{4 85 \times 4 8 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

485 \times 4 8 5^{3}

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

4 85 \times 8 5^{3}

Calculate the product

4 8 5^{4}

Reduce the index of the radical and exponent with 4

85

\frac{4 15001 \times 8 5 ^{3}}{85}

d = \pm \frac{4 15001 \times 8 5 ^{3}}{85}

Separate the equation into 2 possible cases

d = \frac{4 15001 \times 8 5 ^{3}}{85} d = - \frac{4 15001 \times 8 5 ^{3}}{85}

Solution

d_{1} = - \frac{4 15001 \times 8 5 ^{3}}{85}, d_{2} = \frac{4 15001 \times 8 5 ^{3}}{85}

Alternative Form

d_{1} \approx - 3.644814, d_{2} \approx 3.644814

Show Solution