Solve 8k^2 4k-8=0

Question

Solve the equation

k = \frac{3 2}{2}

Alternative Form

k \approx 0.629961

Evaluate

8 k^{2} \times 4 k - 8 = 0

Multiply

More Steps

Evaluate

8 k^{2} \times 4 k

Multiply the terms

32 k^{2} \times k

Multiply the terms with the same base by adding their exponents

32 k^{2 + 1}

Add the numbers

32 k^{3}

32 k^{3} - 8 = 0

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

32 k^{3} = 0 + 8

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

32 k^{3} = 8

Divide both sides

\frac{32 k ^{3}}{32} = \frac{8}{32}

Divide the numbers

k^{3} = \frac{8}{32}

Cancel out the common factor 8

k^{3} = \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 k^{3} = 3 \frac{1}{4}

Calculate

k = 3 \frac{1}{4}

Solution

More Steps

Evaluate

3 \frac{1}{4}

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

\frac{3 1}{3 4}

Simplify the radical expression

\frac{1}{3 4}

Multiply by the Conjugate

\frac{3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 2}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 2}{2}

k = \frac{3 2}{2}

Alternative Form

k \approx 0.629961

Show Solution