Solve dd^3237-2 - ScanMath

Question

Simplify the expression

237 d^{4} - 2

Evaluate

d \times d^{3} \times 237 - 2

Solution

More Steps

Evaluate

d \times d^{3} \times 237

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 237

Add the numbers

d^{4} \times 237

Use the commutative property to reorder the terms

237 d^{4}

237 d^{4} - 2

Show Solution

d_{1} = - \frac{4 2 \times 23 7 ^{3}}{237}, d_{2} = \frac{4 2 \times 23 7 ^{3}}{237}

Alternative Form

d_{1} \approx - 0.303089, d_{2} \approx 0.303089

Evaluate

d \times d^{3} \times 237 - 2

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

d \times d^{3} \times 237 - 2 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 237

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 237

Add the numbers

d^{4} \times 237

Use the commutative property to reorder the terms

237 d^{4}

237 d^{4} - 2 = 0

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

237 d^{4} = 0 + 2

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

237 d^{4} = 2

Divide both sides

\frac{237 d ^{4}}{237} = \frac{2}{237}

Divide the numbers

d^{4} = \frac{2}{237}

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

d = \pm 4 \frac{2}{237}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{237}

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

\frac{4 2}{4 237}

Multiply by the Conjugate

\frac{4 2 \times 4 23 7 ^{3}}{4 237 \times 4 23 7 ^{3}}

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

\frac{4 2 \times 23 7 ^{3}}{4 237 \times 4 23 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

4237 \times 4 23 7^{3}

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

4 237 \times 23 7^{3}

Calculate the product

4 23 7^{4}

Reduce the index of the radical and exponent with 4

237

\frac{4 2 \times 23 7 ^{3}}{237}

d = \pm \frac{4 2 \times 23 7 ^{3}}{237}

Separate the equation into 2 possible cases

d = \frac{4 2 \times 23 7 ^{3}}{237} d = - \frac{4 2 \times 23 7 ^{3}}{237}

Solution

d_{1} = - \frac{4 2 \times 23 7 ^{3}}{237}, d_{2} = \frac{4 2 \times 23 7 ^{3}}{237}

Alternative Form

d_{1} \approx - 0.303089, d_{2} \approx 0.303089

Show Solution