Solve 5707592/d^2300-1000

Question

Simplify the expression

\frac{1712277600 - 1000 d ^{2}}{d ^{2}}

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d = 0

Show Solution

d_{1} = - \frac{2 10701735}{5}, d_{2} = \frac{2 10701735}{5}

Alternative Form

d_{1} \approx - 1308.540255, d_{2} \approx 1308.540255

Evaluate

\frac{5707592}{d ^{2}} \times 300 - 1000

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

\frac{5707592}{d ^{2}} \times 300 - 1000 = 0

The only way a power can not be 0 is when the base not equals 0

\frac{5707592}{d ^{2}} \times 300 - 1000 = 0, d \neq = 0

Calculate

\frac{5707592}{d ^{2}} \times 300 - 1000 = 0

Multiply the terms

More Steps

\frac{1712277600}{d ^{2}} - 1000 = 0

Subtract the terms

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\frac{1712277600 - 1000 d ^{2}}{d ^{2}} = 0

Cross multiply

1712277600 - 1000 d^{2} = d^{2} \times 0

Simplify the equation

1712277600 - 1000 d^{2} = 0

Rewrite the expression

- 1000 d^{2} = - 1712277600

Change the signs on both sides of the equation

1000 d^{2} = 1712277600

Divide both sides

\frac{1000 d ^{2}}{1000} = \frac{1712277600}{1000}

Divide the numbers

d^{2} = \frac{1712277600}{1000}

Cancel out the common factor 200

d^{2} = \frac{8561388}{5}

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

d = \pm \frac{8561388}{5}

Simplify the expression

More Steps

d = \pm \frac{2 10701735}{5}

Separate the equation into 2 possible cases

d = \frac{2 10701735}{5} d = - \frac{2 10701735}{5}

Check if the solution is in the defined range

d = \frac{2 10701735}{5} d = - \frac{2 10701735}{5}, d \neq = 0

Find the intersection of the solution and the defined range

d = \frac{2 10701735}{5} d = - \frac{2 10701735}{5}

Solution

d_{1} = - \frac{2 10701735}{5}, d_{2} = \frac{2 10701735}{5}

Alternative Form

d_{1} \approx - 1308.540255, d_{2} \approx 1308.540255

Show Solution