Solve 8j^2=328j

$$8 j ^ { 2 } = 328 j$$

Solve for j

$$j=41$$

$$j=0$$

Steps Using Factoring

Subtract 328j from both sides.

$$8j^{2}-328j=0$$

Factor out j.

$$j\left(8j-328\right)=0$$

To find equation solutions, solve j=0 and 8j-328=0.

$$j=0 j=41$$

Steps Using the Quadratic Formula

Subtract 328j from both sides.

$$8j^{2}-328j=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -328 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$j=\frac{-\left(-328\right)±\sqrt{\left(-328\right)^{2}}}{2\times 8}$$

Take the square root of \left(-328\right)^{2}.

$$j=\frac{-\left(-328\right)±328}{2\times 8}$$

The opposite of -328 is 328.

$$j=\frac{328±328}{2\times 8}$$

Multiply 2 times 8.

$$j=\frac{328±328}{16}$$

Now solve the equation j=\frac{328±328}{16} when ± is plus. Add 328 to 328.

$$j=\frac{656}{16}$$

Divide 656 by 16.

$$j=41$$

Now solve the equation j=\frac{328±328}{16} when ± is minus. Subtract 328 from 328.

$$j=\frac{0}{16}$$

Divide 0 by 16.

$$j=0$$

The equation is now solved.

$$j=41 j=0$$

Steps for Completing the Square

Subtract 328j from both sides.

$$8j^{2}-328j=0$$

Divide both sides by 8.

$$\frac{8j^{2}-328j}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$j^{2}+\left(-\frac{328}{8}\right)j=\frac{0}{8}$$

Divide -328 by 8.

$$j^{2}-41j=\frac{0}{8}$$

Divide 0 by 8.

$$j^{2}-41j=0$$

Divide -41, the coefficient of the x term, by 2 to get -\frac{41}{2}. Then add the square of -\frac{41}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$j^{2}-41j+\left(-\frac{41}{2}\right)^{2}=\left(-\frac{41}{2}\right)^{2}$$

Square -\frac{41}{2} by squaring both the numerator and the denominator of the fraction.

$$j^{2}-41j+\frac{1681}{4}=\frac{1681}{4}$$

Factor j^{2}-41j+\frac{1681}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(j-\frac{41}{2}\right)^{2}=\frac{1681}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(j-\frac{41}{2}\right)^{2}}=\sqrt{\frac{1681}{4}}$$

Simplify.

$$j-\frac{41}{2}=\frac{41}{2} j-\frac{41}{2}=-\frac{41}{2}$$

Add \frac{41}{2} to both sides of the equation.

$$j=41 j=0$$