Solve (x+24)*(x+2)-30x/2x(x+2)=0

$$\frac{ (x+24) \times (x+2)-30x }{ 2x(x+2) } =0$$

Solve for x (complex solution)

$$x=2+2\sqrt{11}i\approx 2+6.633249581i$$

$$x=-2\sqrt{11}i+2\approx 2-6.633249581i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+2\right).

$$\left(x+24\right)\left(x+2\right)-30x=0$$

Use the distributive property to multiply x+24 by x+2 and combine like terms.

$$x^{2}+26x+48-30x=0$$

Combine 26x and -30x to get -4x.

$$x^{2}-4x+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 48}}{2}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 48}}{2}$$

Multiply -4 times 48.

$$x=\frac{-\left(-4\right)±\sqrt{16-192}}{2}$$

Add 16 to -192.

$$x=\frac{-\left(-4\right)±\sqrt{-176}}{2}$$

Take the square root of -176.

$$x=\frac{-\left(-4\right)±4\sqrt{11}i}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±4\sqrt{11}i}{2}$$

Now solve the equation x=\frac{4±4\sqrt{11}i}{2} when ± is plus. Add 4 to 4i\sqrt{11}.

$$x=\frac{4+4\sqrt{11}i}{2}$$

Divide 4+4i\sqrt{11} by 2.

$$x=2+2\sqrt{11}i$$

Now solve the equation x=\frac{4±4\sqrt{11}i}{2} when ± is minus. Subtract 4i\sqrt{11} from 4.

$$x=\frac{-4\sqrt{11}i+4}{2}$$

Divide 4-4i\sqrt{11} by 2.

$$x=-2\sqrt{11}i+2$$

The equation is now solved.

$$x=2+2\sqrt{11}i x=-2\sqrt{11}i+2$$

Steps for Completing the Square

Variable x cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+2\right).

$$\left(x+24\right)\left(x+2\right)-30x=0$$

Use the distributive property to multiply x+24 by x+2 and combine like terms.

$$x^{2}+26x+48-30x=0$$

Combine 26x and -30x to get -4x.

$$x^{2}-4x+48=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-4x=-48$$

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.

$$x^{2}-4x+\left(-2\right)^{2}=-48+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=-48+4$$

Add -48 to 4.

$$x^{2}-4x+4=-44$$

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

$$\left(x-2\right)^{2}=-44$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{-44}$$

Simplify.

$$x-2=2\sqrt{11}i x-2=-2\sqrt{11}i$$

Add 2 to both sides of the equation.

$$x=2+2\sqrt{11}i x=-2\sqrt{11}i+2$$