Solve x^2+5x*6=0

$$x ^ { 2 } + 5 x \cdot 6 = 0$$

Solve for x

$$x=-30$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(x+5\times 6\right)=0$$

To find equation solutions, solve x=0 and x+30=0.

$$x=0 x=-30$$

Steps Using the Quadratic Formula

Multiply 5 and 6 to get 30.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 30 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-30±\sqrt{30^{2}}}{2}$$

Take the square root of 30^{2}.

$$x=\frac{-30±30}{2}$$

Now solve the equation x=\frac{-30±30}{2} when ± is plus. Add -30 to 30.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-30±30}{2} when ± is minus. Subtract 30 from -30.

$$x=-\frac{60}{2}$$

Divide -60 by 2.

$$x=-30$$

The equation is now solved.

$$x=0 x=-30$$

Steps for Completing the Square

Multiply 5 and 6 to get 30.

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

Divide 30, the coefficient of the x term, by 2 to get 15. Then add the square of 15 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+30x+15^{2}=15^{2}$$

Square 15.

$$x^{2}+30x+225=225$$

Factor x^{2}+30x+225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+15\right)^{2}=225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+15\right)^{2}}=\sqrt{225}$$

Simplify.

$$x+15=15 x+15=-15$$

Subtract 15 from both sides of the equation.

$$x=0 x=-30$$