To find equation solutions, solve $x=0$ and $x+6=0$.
$$x=0$$ $$x=-6$$
Steps Using the Quadratic Formula
Combine $-4x$ and $10x$ to get $6x$.
$$x^{2}+6x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $6$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-6±\sqrt{6^{2}}}{2}$$
Take the square root of $6^{2}$.
$$x=\frac{-6±6}{2}$$
Now solve the equation $x=\frac{-6±6}{2}$ when $±$ is plus. Add $-6$ to $6$.
$$x=\frac{0}{2}$$
Divide $0$ by $2$.
$$x=0$$
Now solve the equation $x=\frac{-6±6}{2}$ when $±$ is minus. Subtract $6$ from $-6$.
$$x=-\frac{12}{2}$$
Divide $-12$ by $2$.
$$x=-6$$
The equation is now solved.
$$x=0$$ $$x=-6$$
Steps for Completing the Square
Combine $-4x$ and $10x$ to get $6x$.
$$x^{2}+6x=0$$
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.
$$x^{2}+6x+3^{2}=3^{2}$$
Square $3$.
$$x^{2}+6x+9=9$$
Factor $x^{2}+6x+9$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.
$$\left(x+3\right)^{2}=9$$
Take the square root of both sides of the equation.
