Solve a-324/a=4

$$a- \frac{ 324 }{ a } =4$$

Solve for a

$$a=2\sqrt{82}+2\approx 20.110770276$$

$$a=2-2\sqrt{82}\approx -16.110770276$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$aa-324=4a$$

Multiply a and a to get a^{2}.

$$a^{2}-324=4a$$

Subtract 4a from both sides.

$$a^{2}-324-4a=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$a^{2}-4a-324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and -324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-324\right)}}{2}$$

Square -4.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\left(-324\right)}}{2}$$

Multiply -4 times -324.

$$a=\frac{-\left(-4\right)±\sqrt{16+1296}}{2}$$

Add 16 to 1296.

$$a=\frac{-\left(-4\right)±\sqrt{1312}}{2}$$

Take the square root of 1312.

$$a=\frac{-\left(-4\right)±4\sqrt{82}}{2}$$

The opposite of -4 is 4.

$$a=\frac{4±4\sqrt{82}}{2}$$

Now solve the equation a=\frac{4±4\sqrt{82}}{2} when ± is plus. Add 4 to 4\sqrt{82}.

$$a=\frac{4\sqrt{82}+4}{2}$$

Divide 4+4\sqrt{82} by 2.

$$a=2\sqrt{82}+2$$

Now solve the equation a=\frac{4±4\sqrt{82}}{2} when ± is minus. Subtract 4\sqrt{82} from 4.

$$a=\frac{4-4\sqrt{82}}{2}$$

Divide 4-4\sqrt{82} by 2.

$$a=2-2\sqrt{82}$$

The equation is now solved.

$$a=2\sqrt{82}+2 a=2-2\sqrt{82}$$

Steps for Completing the Square

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$aa-324=4a$$

Multiply a and a to get a^{2}.

$$a^{2}-324=4a$$

Subtract 4a from both sides.

$$a^{2}-324-4a=0$$

Add 324 to both sides. Anything plus zero gives itself.

$$a^{2}-4a=324$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$a^{2}-4a+\left(-2\right)^{2}=324+\left(-2\right)^{2}$$

Square -2.

$$a^{2}-4a+4=324+4$$

Add 324 to 4.

$$a^{2}-4a+4=328$$

Factor a^{2}-4a+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}.

$$\left(a-2\right)^{2}=328$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a-2\right)^{2}}=\sqrt{328}$$

Simplify.

$$a-2=2\sqrt{82} a-2=-2\sqrt{82}$$

Add 2 to both sides of the equation.

$$a=2\sqrt{82}+2 a=2-2\sqrt{82}$$