Solve dd^32-42-210

Question

Simplify the expression

2 d^{4} - 252

Evaluate

d \times d^{3} \times 2 - 42 - 210

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 2

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 2

Add the numbers

d^{4} \times 2

Use the commutative property to reorder the terms

2 d^{4}

2 d^{4} - 42 - 210

Solution

2 d^{4} - 252

Show Solution

2 (d^{4} - 126)

Evaluate

d \times d^{3} \times 2 - 42 - 210

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 2

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 2

Add the numbers

d^{4} \times 2

Use the commutative property to reorder the terms

2 d^{4}

2 d^{4} - 42 - 210

Subtract the numbers

2 d^{4} - 252

Solution

2 (d^{4} - 126)

Show Solution

d_{1} = - 4126, d_{2} = 4126

Alternative Form

d_{1} \approx - 3.350369, d_{2} \approx 3.350369

Evaluate

d \times d^{3} \times 2 - 42 - 210

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

d \times d^{3} \times 2 - 42 - 210 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 2

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 2

Add the numbers

d^{4} \times 2

Use the commutative property to reorder the terms

2 d^{4}

2 d^{4} - 42 - 210 = 0

Subtract the numbers

2 d^{4} - 252 = 0

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

2 d^{4} = 0 + 252

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

2 d^{4} = 252

Divide both sides

\frac{2 d ^{4}}{2} = \frac{252}{2}

Divide the numbers

d^{4} = \frac{252}{2}

Divide the numbers

More Steps

Evaluate

\frac{252}{2}

Reduce the numbers

\frac{126}{1}

Calculate

126

d^{4} = 126

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

d = \pm 4126

Separate the equation into 2 possible cases

d = 4126 d = - 4126

Solution

d_{1} = - 4126, d_{2} = 4126

Alternative Form

d_{1} \approx - 3.350369, d_{2} \approx 3.350369

Show Solution