Solve k^2511-16600

Question

Simplify the expression

511 k^{2} - 16600

Evaluate

k^{2} \times 511 - 16600

Solution

511 k^{2} - 16600

Show Solution

k_{1} = - \frac{10 84826}{511}, k_{2} = \frac{10 84826}{511}

Alternative Form

k_{1} \approx - 5.69959, k_{2} \approx 5.69959

Evaluate

k^{2} \times 511 - 16600

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

k^{2} \times 511 - 16600 = 0

Use the commutative property to reorder the terms

511 k^{2} - 16600 = 0

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

511 k^{2} = 0 + 16600

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

511 k^{2} = 16600

Divide both sides

\frac{511 k ^{2}}{511} = \frac{16600}{511}

Divide the numbers

k^{2} = \frac{16600}{511}

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

k = \pm \frac{16600}{511}

Simplify the expression

More Steps

Evaluate

\frac{16600}{511}

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

\frac{16600}{511}

Simplify the radical expression

More Steps

Evaluate

16600

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

100 \times 166

Write the number in exponential form with the base of 10

1 0^{2} \times 166

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

1 0^{2} \times 166

Reduce the index of the radical and exponent with 2

10166

\frac{10 166}{511}

Multiply by the Conjugate

\frac{10 166 \times 511}{511 \times 511}

Multiply the numbers

More Steps

Evaluate

166 \times 511

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

166 \times 511

Calculate the product

84826

\frac{10 84826}{511 \times 511}

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

\frac{10 84826}{511}

k = \pm \frac{10 84826}{511}

Separate the equation into 2 possible cases

k = \frac{10 84826}{511} k = - \frac{10 84826}{511}

Solution

k_{1} = - \frac{10 84826}{511}, k_{2} = \frac{10 84826}{511}

Alternative Form

k_{1} \approx - 5.69959, k_{2} \approx 5.69959

Show Solution