Solve 2div(x-6)=4quadx=

$$2 \div ( x - 6 ) = 4 \quad x =$$

Solve for x

$$x=\frac{\sqrt{38}}{2}+3\approx 6.082207001$$

$$x=-\frac{\sqrt{38}}{2}+3\approx -0.082207001$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$2=4x\left(x-6\right)$$

Use the distributive property to multiply 4x by x-6.

$$2=4x^{2}-24x$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}-24x=2$$

Subtract 2 from both sides.

$$4x^{2}-24x-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -24 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 4\left(-2\right)}}{2\times 4}$$

Square -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 4\left(-2\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\left(-24\right)±\sqrt{576-16\left(-2\right)}}{2\times 4}$$

Multiply -16 times -2.

$$x=\frac{-\left(-24\right)±\sqrt{576+32}}{2\times 4}$$

Add 576 to 32.

$$x=\frac{-\left(-24\right)±\sqrt{608}}{2\times 4}$$

Take the square root of 608.

$$x=\frac{-\left(-24\right)±4\sqrt{38}}{2\times 4}$$

The opposite of -24 is 24.

$$x=\frac{24±4\sqrt{38}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{24±4\sqrt{38}}{8}$$

Now solve the equation x=\frac{24±4\sqrt{38}}{8} when ± is plus. Add 24 to 4\sqrt{38}.

$$x=\frac{4\sqrt{38}+24}{8}$$

Divide 24+4\sqrt{38} by 8.

$$x=\frac{\sqrt{38}}{2}+3$$

Now solve the equation x=\frac{24±4\sqrt{38}}{8} when ± is minus. Subtract 4\sqrt{38} from 24.

$$x=\frac{24-4\sqrt{38}}{8}$$

Divide 24-4\sqrt{38} by 8.

$$x=-\frac{\sqrt{38}}{2}+3$$

The equation is now solved.

$$x=\frac{\sqrt{38}}{2}+3 x=-\frac{\sqrt{38}}{2}+3$$

Steps for Completing the Square

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$2=4x\left(x-6\right)$$

Use the distributive property to multiply 4x by x-6.

$$2=4x^{2}-24x$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}-24x=2$$

Divide both sides by 4.

$$\frac{4x^{2}-24x}{4}=\frac{2}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{24}{4}\right)x=\frac{2}{4}$$

Divide -24 by 4.

$$x^{2}-6x=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}-6x=\frac{1}{2}$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=\frac{1}{2}+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=\frac{1}{2}+9$$

Add \frac{1}{2} to 9.

$$x^{2}-6x+9=\frac{19}{2}$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=\frac{19}{2}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{\frac{19}{2}}$$

Simplify.

$$x-3=\frac{\sqrt{38}}{2} x-3=-\frac{\sqrt{38}}{2}$$

Add 3 to both sides of the equation.

$$x=\frac{\sqrt{38}}{2}+3 x=-\frac{\sqrt{38}}{2}+3$$