Solve 96370-r^2200

Question

Simplify the expression

96370 - 200 r^{2}

Evaluate

96370 - r^{2} \times 200

Solution

96370 - 200 r^{2}

Show Solution

10 (9637 - 20 r^{2})

Evaluate

96370 - r^{2} \times 200

Use the commutative property to reorder the terms

96370 - 200 r^{2}

Solution

10 (9637 - 20 r^{2})

Show Solution

r_{1} = - \frac{48185}{10}, r_{2} = \frac{48185}{10}

Alternative Form

r_{1} \approx - 21.951082, r_{2} \approx 21.951082

Evaluate

96370 - r^{2} \times 200

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

96370 - r^{2} \times 200 = 0

Use the commutative property to reorder the terms

96370 - 200 r^{2} = 0

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

- 200 r^{2} = 0 - 96370

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

- 200 r^{2} = - 96370

Change the signs on both sides of the equation

200 r^{2} = 96370

Divide both sides

\frac{200 r ^{2}}{200} = \frac{96370}{200}

Divide the numbers

r^{2} = \frac{96370}{200}

Cancel out the common factor 10

r^{2} = \frac{9637}{20}

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

r = \pm \frac{9637}{20}

Simplify the expression

More Steps

Evaluate

\frac{9637}{20}

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

\frac{9637}{20}

Simplify the radical expression

More Steps

Evaluate

20

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

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

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

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{9637}{2 5}

Multiply by the Conjugate

\frac{9637 \times 5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

9637 \times 5

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

9637 \times 5

Calculate the product

48185

\frac{48185}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

25 \times 5

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

2 \times 5

Multiply the terms

10

\frac{48185}{10}

r = \pm \frac{48185}{10}

Separate the equation into 2 possible cases

r = \frac{48185}{10} r = - \frac{48185}{10}

Solution

r_{1} = - \frac{48185}{10}, r_{2} = \frac{48185}{10}

Alternative Form

r_{1} \approx - 21.951082, r_{2} \approx 21.951082

Show Solution