Solve 92k^2=78k

$$92 k ^ { 2 } = 78 k$$

Solve for k

$$k=\frac{39}{46}\approx 0.847826087$$

$$k=0$$

Steps Using Factoring

Subtract 78k from both sides.

$$92k^{2}-78k=0$$

Factor out k.

$$k\left(92k-78\right)=0$$

To find equation solutions, solve k=0 and 92k-78=0.

$$k=0 k=\frac{39}{46}$$

Steps Using the Quadratic Formula

Subtract 78k from both sides.

$$92k^{2}-78k=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 92 for a, -78 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{-\left(-78\right)±\sqrt{\left(-78\right)^{2}}}{2\times 92}$$

Take the square root of \left(-78\right)^{2}.

$$k=\frac{-\left(-78\right)±78}{2\times 92}$$

The opposite of -78 is 78.

$$k=\frac{78±78}{2\times 92}$$

Multiply 2 times 92.

$$k=\frac{78±78}{184}$$

Now solve the equation k=\frac{78±78}{184} when ± is plus. Add 78 to 78.

$$k=\frac{156}{184}$$

Reduce the fraction \frac{156}{184} to lowest terms by extracting and canceling out 4.

$$k=\frac{39}{46}$$

Now solve the equation k=\frac{78±78}{184} when ± is minus. Subtract 78 from 78.

$$k=\frac{0}{184}$$

Divide 0 by 184.

$$k=0$$

The equation is now solved.

$$k=\frac{39}{46} k=0$$

Steps for Completing the Square

Subtract 78k from both sides.

$$92k^{2}-78k=0$$

Divide both sides by 92.

$$\frac{92k^{2}-78k}{92}=\frac{0}{92}$$

Dividing by 92 undoes the multiplication by 92.

$$k^{2}+\left(-\frac{78}{92}\right)k=\frac{0}{92}$$

Reduce the fraction \frac{-78}{92} to lowest terms by extracting and canceling out 2.

$$k^{2}-\frac{39}{46}k=\frac{0}{92}$$

Divide 0 by 92.

$$k^{2}-\frac{39}{46}k=0$$

Divide -\frac{39}{46}, the coefficient of the x term, by 2 to get -\frac{39}{92}. Then add the square of -\frac{39}{92} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$k^{2}-\frac{39}{46}k+\left(-\frac{39}{92}\right)^{2}=\left(-\frac{39}{92}\right)^{2}$$

Square -\frac{39}{92} by squaring both the numerator and the denominator of the fraction.

$$k^{2}-\frac{39}{46}k+\frac{1521}{8464}=\frac{1521}{8464}$$

Factor k^{2}-\frac{39}{46}k+\frac{1521}{8464}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(k-\frac{39}{92}\right)^{2}=\frac{1521}{8464}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(k-\frac{39}{92}\right)^{2}}=\sqrt{\frac{1521}{8464}}$$

Simplify.

$$k-\frac{39}{92}=\frac{39}{92} k-\frac{39}{92}=-\frac{39}{92}$$

Add \frac{39}{92} to both sides of the equation.

$$k=\frac{39}{46} k=0$$