Solve Using the Square Root Property 4k^2=5k

$4 k^{2} = 5 k$

Step 1

Subtract $5 k$ from both sides of the equation.

$4 k^{2} - 5 k = 0$

Step 2

Factor $k$ out of $4 k^{2} - 5 k$ .

Factor $k$ out of $4 k^{2}$ .

$k (4 k) - 5 k = 0$

Factor $k$ out of $- 5 k$ .

$k (4 k) + k \cdot - 5 = 0$

Factor $k$ out of $k (4 k) + k \cdot - 5$ .

$k (4 k - 5) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$k = 0$

$4 k - 5 = 0$

Step 4

Set $k$ equal to $0$ .

$k = 0$

Step 5

Set $4 k - 5$ equal to $0$ and solve for $k$ .

Set $4 k - 5$ equal to $0$ .

$4 k - 5 = 0$

Solve $4 k - 5 = 0$ for $k$ .

Add $5$ to both sides of the equation.

$4 k = 5$

Divide each term in $4 k = 5$ by $4$ and simplify.

Divide each term in $4 k = 5$ by $4$ .

$\frac{4 k}{4} = \frac{5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 k}{4} = \frac{5}{4}$

Divide $k$ by $1$ .

$k = \frac{5}{4}$

Step 6

The final solution is all the values that make $k (4 k - 5) = 0$ true.

$k = 0, \frac{5}{4}$