Solve 3k^2260721-3-3

Question

Simplify the expression

782163 k^{2} - 6

Evaluate

3 k^{2} \times 260721 - 3 - 3

Multiply the terms

782163 k^{2} - 3 - 3

Solution

782163 k^{2} - 6

Show Solution

3 (260721 k^{2} - 2)

Evaluate

3 k^{2} \times 260721 - 3 - 3

Multiply the terms

782163 k^{2} - 3 - 3

Subtract the numbers

782163 k^{2} - 6

Solution

3 (260721 k^{2} - 2)

Show Solution

k_{1} = - \frac{57938}{86907}, k_{2} = \frac{57938}{86907}

Alternative Form

k_{1} \approx - 0.00277, k_{2} \approx 0.00277

Evaluate

3 k^{2} \times 260721 - 3 - 3

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

3 k^{2} \times 260721 - 3 - 3 = 0

Multiply the terms

782163 k^{2} - 3 - 3 = 0

Subtract the numbers

782163 k^{2} - 6 = 0

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

782163 k^{2} = 0 + 6

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

782163 k^{2} = 6

Divide both sides

\frac{782163 k ^{2}}{782163} = \frac{6}{782163}

Divide the numbers

k^{2} = \frac{6}{782163}

Cancel out the common factor 3

k^{2} = \frac{2}{260721}

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

k = \pm \frac{2}{260721}

Simplify the expression

More Steps

Evaluate

\frac{2}{260721}

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

\frac{2}{260721}

Simplify the radical expression

More Steps

Evaluate

260721

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

9 \times 28969

Write the number in exponential form with the base of 3

3^{2} \times 28969

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

3^{2} \times 28969

Reduce the index of the radical and exponent with 2

328969

\frac{2}{3 28969}

Multiply by the Conjugate

\frac{2 \times 28969}{3 28969 \times 28969}

Multiply the numbers

More Steps

Evaluate

2 \times 28969

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

2 \times 28969

Calculate the product

57938

\frac{57938}{3 28969 \times 28969}

Multiply the numbers

More Steps

Evaluate

328969 \times 28969

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

3 \times 28969

Multiply the terms

86907

\frac{57938}{86907}

k = \pm \frac{57938}{86907}

Separate the equation into 2 possible cases

k = \frac{57938}{86907} k = - \frac{57938}{86907}

Solution

k_{1} = - \frac{57938}{86907}, k_{2} = \frac{57938}{86907}

Alternative Form

k_{1} \approx - 0.00277, k_{2} \approx 0.00277

Show Solution