Solve 285-50 r^22

Question

Simplify the expression

285 - 100 r^{2}

Evaluate

285 - 50 r^{2} \times 2

Solution

285 - 100 r^{2}

Show Solution

5 (57 - 20 r^{2})

Evaluate

285 - 50 r^{2} \times 2

Multiply the terms

285 - 100 r^{2}

Solution

5 (57 - 20 r^{2})

Show Solution

r_{1} = - \frac{285}{10}, r_{2} = \frac{285}{10}

Alternative Form

r_{1} \approx - 1.688194, r_{2} \approx 1.688194

Evaluate

285 - 50 r^{2} \times 2

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

285 - 50 r^{2} \times 2 = 0

Multiply the terms

285 - 100 r^{2} = 0

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

- 100 r^{2} = 0 - 285

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

- 100 r^{2} = - 285

Change the signs on both sides of the equation

100 r^{2} = 285

Divide both sides

\frac{100 r ^{2}}{100} = \frac{285}{100}

Divide the numbers

r^{2} = \frac{285}{100}

Cancel out the common factor 5

r^{2} = \frac{57}{20}

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

r = \pm \frac{57}{20}

Simplify the expression

More Steps

Evaluate

\frac{57}{20}

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

\frac{57}{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{57}{2 5}

Multiply by the Conjugate

\frac{57 \times 5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

57 \times 5

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

57 \times 5

Calculate the product

285

\frac{285}{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{285}{10}

r = \pm \frac{285}{10}

Separate the equation into 2 possible cases

r = \frac{285}{10} r = - \frac{285}{10}

Solution

r_{1} = - \frac{285}{10}, r_{2} = \frac{285}{10}

Alternative Form

r_{1} \approx - 1.688194, r_{2} \approx 1.688194

Show Solution