Solve 24k^2-107k^64

Question

Simplify the expression

24 k^{2} - 428 k^{6}

Evaluate

24 k^{2} - 107 k^{6} \times 4

Solution

24 k^{2} - 428 k^{6}

Show Solution

4 k^{2} (6 - 107 k^{4})

Evaluate

24 k^{2} - 107 k^{6} \times 4

Multiply the terms

24 k^{2} - 428 k^{6}

Rewrite the expression

4 k^{2} \times 6 - 4 k^{2} \times 107 k^{4}

Solution

4 k^{2} (6 - 107 k^{4})

Show Solution

k_{1} = - \frac{4 6 \times 10 7 ^{3}}{107}, k_{2} = 0, k_{3} = \frac{4 6 \times 10 7 ^{3}}{107}

Alternative Form

k_{1} \approx - 0.486622, k_{2} = 0, k_{3} \approx 0.486622

Evaluate

24 k^{2} - 107 k^{6} \times 4

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

24 k^{2} - 107 k^{6} \times 4 = 0

Multiply the terms

24 k^{2} - 428 k^{6} = 0

Factor the expression

4 k^{2} (6 - 107 k^{4}) = 0

Divide both sides

k^{2} (6 - 107 k^{4}) = 0

Separate the equation into 2 possible cases

k^{2} = 0 6 - 107 k^{4} = 0

The only way a power can be 0 is when the base equals 0

k = 0 6 - 107 k^{4} = 0

Solve the equation

More Steps

Evaluate

6 - 107 k^{4} = 0

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

- 107 k^{4} = 0 - 6

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

- 107 k^{4} = - 6

Change the signs on both sides of the equation

107 k^{4} = 6

Divide both sides

\frac{107 k ^{4}}{107} = \frac{6}{107}

Divide the numbers

k^{4} = \frac{6}{107}

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

k = \pm 4 \frac{6}{107}

Simplify the expression

More Steps

Evaluate

4 \frac{6}{107}

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

\frac{4 6}{4 107}

Multiply by the Conjugate

\frac{4 6 \times 4 10 7 ^{3}}{4 107 \times 4 10 7 ^{3}}

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

\frac{4 6 \times 10 7 ^{3}}{4 107 \times 4 10 7 ^{3}}

Multiply the numbers

\frac{4 6 \times 10 7 ^{3}}{107}

k = \pm \frac{4 6 \times 10 7 ^{3}}{107}

Separate the equation into 2 possible cases

k = \frac{4 6 \times 10 7 ^{3}}{107} k = - \frac{4 6 \times 10 7 ^{3}}{107}

k = 0 k = \frac{4 6 \times 10 7 ^{3}}{107} k = - \frac{4 6 \times 10 7 ^{3}}{107}

Solution

k_{1} = - \frac{4 6 \times 10 7 ^{3}}{107}, k_{2} = 0, k_{3} = \frac{4 6 \times 10 7 ^{3}}{107}

Alternative Form

k_{1} \approx - 0.486622, k_{2} = 0, k_{3} \approx 0.486622

Show Solution