Solve 56x=x^2

$$56x= { x }^{ 2 }$$

Solve for x

$$x=56$$

$$x=0$$

Steps Using Factoring

Subtract x^{2} from both sides.

$$56x-x^{2}=0$$

Factor out x.

$$x\left(56-x\right)=0$$

To find equation solutions, solve x=0 and 56-x=0.

$$x=0 x=56$$

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$56x-x^{2}=0$$

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.

$$-x^{2}+56x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 56 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-56±\sqrt{56^{2}}}{2\left(-1\right)}$$

Take the square root of 56^{2}.

$$x=\frac{-56±56}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-56±56}{-2}$$

Now solve the equation x=\frac{-56±56}{-2} when ± is plus. Add -56 to 56.

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

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-56±56}{-2} when ± is minus. Subtract 56 from -56.

$$x=-\frac{112}{-2}$$

Divide -112 by -2.

$$x=56$$

The equation is now solved.

$$x=0 x=56$$

Steps for Completing the Square

Subtract x^{2} from both sides.

$$56x-x^{2}=0$$

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.

$$-x^{2}+56x=0$$

Divide both sides by -1.

$$\frac{-x^{2}+56x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{56}{-1}x=\frac{0}{-1}$$

Divide 56 by -1.

$$x^{2}-56x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}-56x=0$$

Divide -56, the coefficient of the x term, by 2 to get -28. Then add the square of -28 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-56x+\left(-28\right)^{2}=\left(-28\right)^{2}$$

Square -28.

$$x^{2}-56x+784=784$$

Factor x^{2}-56x+784. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-28\right)^{2}=784$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-28\right)^{2}}=\sqrt{784}$$

Simplify.

$$x-28=28 x-28=-28$$

Add 28 to both sides of the equation.

$$x=56 x=0$$