Solve d^45-9-102 - ScanMath

Question

Simplify the expression

5 d^{4} - 111

Evaluate

d^{4} \times 5 - 9 - 102

Use the commutative property to reorder the terms

5 d^{4} - 9 - 102

Solution

5 d^{4} - 111

Show Solution

d_{1} = - \frac{4 13875}{5}, d_{2} = \frac{4 13875}{5}

Alternative Form

d_{1} \approx - 2.170642, d_{2} \approx 2.170642

Evaluate

d^{4} \times 5 - 9 - 102

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

d^{4} \times 5 - 9 - 102 = 0

Use the commutative property to reorder the terms

5 d^{4} - 9 - 102 = 0

Subtract the numbers

5 d^{4} - 111 = 0

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

5 d^{4} = 0 + 111

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

5 d^{4} = 111

Divide both sides

\frac{5 d ^{4}}{5} = \frac{111}{5}

Divide the numbers

d^{4} = \frac{111}{5}

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

d = \pm 4 \frac{111}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{111}{5}

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

\frac{4 111}{4 5}

Multiply by the Conjugate

\frac{4 111 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 111 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

4111 \times 4125

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

4 111 \times 125

Calculate the product

413875

\frac{4 13875}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 13875}{5}

d = \pm \frac{4 13875}{5}

Separate the equation into 2 possible cases

d = \frac{4 13875}{5} d = - \frac{4 13875}{5}

Solution

d_{1} = - \frac{4 13875}{5}, d_{2} = \frac{4 13875}{5}

Alternative Form

d_{1} \approx - 2.170642, d_{2} \approx 2.170642

Show Solution