Solve 92402-1r^220

Question

Simplify the expression

92402 - 20 r^{2}

Evaluate

92402 - 1 \times r^{2} \times 20

Solution

More Steps

Evaluate

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92402 - 20 r^{2}

Show Solution

2 (46201 - 10 r^{2})

Evaluate

92402 - 1 \times r^{2} \times 20

Multiply the terms

More Steps

Evaluate

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92402 - 20 r^{2}

Solution

2 (46201 - 10 r^{2})

Show Solution

r_{1} = - \frac{462010}{10}, r_{2} = \frac{462010}{10}

Alternative Form

r_{1} \approx - 67.971317, r_{2} \approx 67.971317

Evaluate

92402 - 1 \times r^{2} \times 20

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

92402 - 1 \times r^{2} \times 20 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92402 - 20 r^{2} = 0

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

- 20 r^{2} = 0 - 92402

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

- 20 r^{2} = - 92402

Change the signs on both sides of the equation

20 r^{2} = 92402

Divide both sides

\frac{20 r ^{2}}{20} = \frac{92402}{20}

Divide the numbers

r^{2} = \frac{92402}{20}

Cancel out the common factor 2

r^{2} = \frac{46201}{10}

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

r = \pm \frac{46201}{10}

Simplify the expression

More Steps

Evaluate

\frac{46201}{10}

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

\frac{46201}{10}

Multiply by the Conjugate

\frac{46201 \times 10}{10 \times 10}

Multiply the numbers

More Steps

Evaluate

46201 \times 10

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

46201 \times 10

Calculate the product

462010

\frac{462010}{10 \times 10}

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

\frac{462010}{10}

r = \pm \frac{462010}{10}

Separate the equation into 2 possible cases

r = \frac{462010}{10} r = - \frac{462010}{10}

Solution

r_{1} = - \frac{462010}{10}, r_{2} = \frac{462010}{10}

Alternative Form

r_{1} \approx - 67.971317, r_{2} \approx 67.971317

Show Solution