Solve 32102-9d^4 - ScanMath

Question

Find the roots

d_{1} = - \frac{4 288918}{3}, d_{2} = \frac{4 288918}{3}

Alternative Form

d_{1} \approx - 7.728094, d_{2} \approx 7.728094

Evaluate

32102 - 9 d^{4}

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

32102 - 9 d^{4} = 0

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

- 9 d^{4} = 0 - 32102

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

- 9 d^{4} = - 32102

Change the signs on both sides of the equation

9 d^{4} = 32102

Divide both sides

\frac{9 d ^{4}}{9} = \frac{32102}{9}

Divide the numbers

d^{4} = \frac{32102}{9}

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

d = \pm 4 \frac{32102}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{32102}{9}

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

\frac{4 32102}{4 9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4 32102}{3}

Multiply by the Conjugate

\frac{4 32102 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

432102 \times 3

Use n a = mn a^{m} to expand the expression

432102 \times 4 3^{2}

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

4 32102 \times 3^{2}

Calculate the product

4288918

\frac{4 288918}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 288918}{3}

d = \pm \frac{4 288918}{3}

Separate the equation into 2 possible cases

d = \frac{4 288918}{3} d = - \frac{4 288918}{3}

Solution

d_{1} = - \frac{4 288918}{3}, d_{2} = \frac{4 288918}{3}

Alternative Form

d_{1} \approx - 7.728094, d_{2} \approx 7.728094

Show Solution