Solve x*(48-3x)=240

$$x \times (48-3x)=240$$

Solve for x (complex solution)

$$x=8+4i$$

$$x=8-4i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by 48-3x.

$$48x-3x^{2}=240$$

Subtract 240 from both sides.

$$48x-3x^{2}-240=0$$

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.

$$-3x^{2}+48x-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 48 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-48±\sqrt{48^{2}-4\left(-3\right)\left(-240\right)}}{2\left(-3\right)}$$

Square 48.

$$x=\frac{-48±\sqrt{2304-4\left(-3\right)\left(-240\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{-48±\sqrt{2304+12\left(-240\right)}}{2\left(-3\right)}$$

Multiply 12 times -240.

$$x=\frac{-48±\sqrt{2304-2880}}{2\left(-3\right)}$$

Add 2304 to -2880.

$$x=\frac{-48±\sqrt{-576}}{2\left(-3\right)}$$

Take the square root of -576.

$$x=\frac{-48±24i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{-48±24i}{-6}$$

Now solve the equation x=\frac{-48±24i}{-6} when ± is plus. Add -48 to 24i.

$$x=\frac{-48+24i}{-6}$$

Divide -48+24i by -6.

$$x=8-4i$$

Now solve the equation x=\frac{-48±24i}{-6} when ± is minus. Subtract 24i from -48.

$$x=\frac{-48-24i}{-6}$$

Divide -48-24i by -6.

$$x=8+4i$$

The equation is now solved.

$$x=8-4i x=8+4i$$

Steps for Completing the Square

Use the distributive property to multiply x by 48-3x.

$$48x-3x^{2}=240$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-3x^{2}+48x=240$$

Divide both sides by -3.

$$\frac{-3x^{2}+48x}{-3}=\frac{240}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x^{2}+\frac{48}{-3}x=\frac{240}{-3}$$

Divide 48 by -3.

$$x^{2}-16x=\frac{240}{-3}$$

Divide 240 by -3.

$$x^{2}-16x=-80$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=-80+\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=-80+64$$

Add -80 to 64.

$$x^{2}-16x+64=-16$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=-16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{-16}$$

Simplify.

$$x-8=4i x-8=-4i$$

Add 8 to both sides of the equation.

$$x=8+4i x=8-4i$$