To find equation solutions, solve $x=0$ and $-x+7=0$.
$$x=0$$ $$x=7$$
Steps Using the Quadratic Formula
Subtract $2$ from both sides.
$$2-x^{2}-2=-7x$$
Subtract $2$ from $2$ to get $0$.
$$-x^{2}=-7x$$
Add $7x$ to both sides.
$$-x^{2}+7x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $7$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-7±\sqrt{7^{2}}}{2\left(-1\right)}$$
Take the square root of $7^{2}$.
$$x=\frac{-7±7}{2\left(-1\right)}$$
Multiply $2$ times $-1$.
$$x=\frac{-7±7}{-2}$$
Now solve the equation $x=\frac{-7±7}{-2}$ when $±$ is plus. Add $-7$ to $7$.
$$x=\frac{0}{-2}$$
Divide $0$ by $-2$.
$$x=0$$
Now solve the equation $x=\frac{-7±7}{-2}$ when $±$ is minus. Subtract $7$ from $-7$.
$$x=-\frac{14}{-2}$$
Divide $-14$ by $-2$.
$$x=7$$
The equation is now solved.
$$x=0$$ $$x=7$$
Steps for Completing the Square
Add $7x$ to both sides.
$$2-x^{2}+7x=2$$
Subtract $2$ from both sides.
$$-x^{2}+7x=2-2$$
Subtract $2$ from $2$ to get $0$.
$$-x^{2}+7x=0$$
Divide both sides by $-1$.
$$\frac{-x^{2}+7x}{-1}=\frac{0}{-1}$$
Dividing by $-1$ undoes the multiplication by $-1$.
$$x^{2}+\frac{7}{-1}x=\frac{0}{-1}$$
Divide $7$ by $-1$.
$$x^{2}-7x=\frac{0}{-1}$$
Divide $0$ by $-1$.
$$x^{2}-7x=0$$
Divide $-7$, the coefficient of the $x$ term, by $2$ to get $-\frac{7}{2}$. Then add the square of $-\frac{7}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
