Solve d^48-2-535 - ScanMath

Question

Simplify the expression

8 d^{4} - 537

Evaluate

d^{4} \times 8 - 2 - 535

Use the commutative property to reorder the terms

8 d^{4} - 2 - 535

Solution

8 d^{4} - 537

Show Solution

d_{1} = - \frac{4 1074}{2}, d_{2} = \frac{4 1074}{2}

Alternative Form

d_{1} \approx - 2.862339, d_{2} \approx 2.862339

Evaluate

d^{4} \times 8 - 2 - 535

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

d^{4} \times 8 - 2 - 535 = 0

Use the commutative property to reorder the terms

8 d^{4} - 2 - 535 = 0

Subtract the numbers

8 d^{4} - 537 = 0

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

8 d^{4} = 0 + 537

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

8 d^{4} = 537

Divide both sides

\frac{8 d ^{4}}{8} = \frac{537}{8}

Divide the numbers

d^{4} = \frac{537}{8}

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

d = \pm 4 \frac{537}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{537}{8}

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

\frac{4 537}{4 8}

Multiply by the Conjugate

\frac{4 537 \times 4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{4 537 \times 2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

4537 \times 2^{2} 42

Multiply the terms

41074 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 41074

\frac{2 ^{2} 4 1074}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4 8^{3}

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

4 8 \times 8^{3}

Calculate the product

4 8^{4}

Transform the expression

4 2^{12}

Reduce the index of the radical and exponent with 4

2^{3}

\frac{2 ^{2} 4 1074}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{4 1074}{2}

d = \pm \frac{4 1074}{2}

Separate the equation into 2 possible cases

d = \frac{4 1074}{2} d = - \frac{4 1074}{2}

Solution

d_{1} = - \frac{4 1074}{2}, d_{2} = \frac{4 1074}{2}

Alternative Form

d_{1} \approx - 2.862339, d_{2} \approx 2.862339

Show Solution