Solve 43000-2d^230

Question

Simplify the expression

43000 - 60 d^{2}

Evaluate

43000 - 2 d^{2} \times 30

Solution

43000 - 60 d^{2}

Show Solution

20 (2150 - 3 d^{2})

Evaluate

43000 - 2 d^{2} \times 30

Multiply the terms

43000 - 60 d^{2}

Solution

20 (2150 - 3 d^{2})

Show Solution

d_{1} = - \frac{5 258}{3}, d_{2} = \frac{5 258}{3}

Alternative Form

d_{1} \approx - 26.770631, d_{2} \approx 26.770631

Evaluate

43000 - 2 d^{2} \times 30

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

43000 - 2 d^{2} \times 30 = 0

Multiply the terms

43000 - 60 d^{2} = 0

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

- 60 d^{2} = 0 - 43000

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

- 60 d^{2} = - 43000

Change the signs on both sides of the equation

60 d^{2} = 43000

Divide both sides

\frac{60 d ^{2}}{60} = \frac{43000}{60}

Divide the numbers

d^{2} = \frac{43000}{60}

Cancel out the common factor 20

d^{2} = \frac{2150}{3}

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

d = \pm \frac{2150}{3}

Simplify the expression

More Steps

Evaluate

\frac{2150}{3}

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

\frac{2150}{3}

Simplify the radical expression

More Steps

Evaluate

2150

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 86

Write the number in exponential form with the base of 5

5^{2} \times 86

The root of a product is equal to the product of the roots of each factor

5^{2} \times 86

Reduce the index of the radical and exponent with 2

586

\frac{5 86}{3}

Multiply by the Conjugate

\frac{5 86 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

86 \times 3

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

86 \times 3

Calculate the product

258

\frac{5 258}{3 \times 3}

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

\frac{5 258}{3}

d = \pm \frac{5 258}{3}

Separate the equation into 2 possible cases

d = \frac{5 258}{3} d = - \frac{5 258}{3}

Solution

d_{1} = - \frac{5 258}{3}, d_{2} = \frac{5 258}{3}

Alternative Form

d_{1} \approx - 26.770631, d_{2} \approx 26.770631

Show Solution