Solve 5x(x+6)=-50

$$5 x ( x + 6 ) = - 50$$

Solve for x (complex solution)

$$x=-3+i$$

$$x=-3-i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x by x+6.

$$5x^{2}+30x=-50$$

Add 50 to both sides.

$$5x^{2}+30x+50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 30 for b, and 50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-30±\sqrt{30^{2}-4\times 5\times 50}}{2\times 5}$$

Square 30.

$$x=\frac{-30±\sqrt{900-4\times 5\times 50}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-30±\sqrt{900-20\times 50}}{2\times 5}$$

Multiply -20 times 50.

$$x=\frac{-30±\sqrt{900-1000}}{2\times 5}$$

Add 900 to -1000.

$$x=\frac{-30±\sqrt{-100}}{2\times 5}$$

Take the square root of -100.

$$x=\frac{-30±10i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-30±10i}{10}$$

Now solve the equation x=\frac{-30±10i}{10} when ± is plus. Add -30 to 10i.

$$x=\frac{-30+10i}{10}$$

Divide -30+10i by 10.

$$x=-3+i$$

Now solve the equation x=\frac{-30±10i}{10} when ± is minus. Subtract 10i from -30.

$$x=\frac{-30-10i}{10}$$

Divide -30-10i by 10.

$$x=-3-i$$

The equation is now solved.

$$x=-3+i x=-3-i$$

Steps for Completing the Square

Use the distributive property to multiply 5x by x+6.

$$5x^{2}+30x=-50$$

Divide both sides by 5.

$$\frac{5x^{2}+30x}{5}=-\frac{50}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{30}{5}x=-\frac{50}{5}$$

Divide 30 by 5.

$$x^{2}+6x=-\frac{50}{5}$$

Divide -50 by 5.

$$x^{2}+6x=-10$$

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.

$$x^{2}+6x+3^{2}=-10+3^{2}$$

Square 3.

$$x^{2}+6x+9=-10+9$$

Add -10 to 9.

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

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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+3=i x+3=-i$$

Subtract 3 from both sides of the equation.

$$x=-3+i x=-3-i$$