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