Solve (x)=x^2-15x

$$( x ) = x ^ { 2 } - 15 x$$

Solve for x

$$x=16$$

$$x=0$$

Steps Using Factoring

Subtract x^{2} from both sides.

$$x-x^{2}=-15x$$

Add 15x to both sides.

$$x-x^{2}+15x=0$$

Combine x and 15x to get 16x.

$$16x-x^{2}=0$$

Factor out x.

$$x\left(16-x\right)=0$$

To find equation solutions, solve x=0 and 16-x=0.

$$x=0 x=16$$

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$x-x^{2}=-15x$$

Add 15x to both sides.

$$x-x^{2}+15x=0$$

Combine x and 15x to get 16x.

$$16x-x^{2}=0$$

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.

$$-x^{2}+16x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 16 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}}}{2\left(-1\right)}$$

Take the square root of 16^{2}.

$$x=\frac{-16±16}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-16±16}{-2}$$

Now solve the equation x=\frac{-16±16}{-2} when ± is plus. Add -16 to 16.

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

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-16±16}{-2} when ± is minus. Subtract 16 from -16.

$$x=-\frac{32}{-2}$$

Divide -32 by -2.

$$x=16$$

The equation is now solved.

$$x=0 x=16$$

Steps for Completing the Square

Subtract x^{2} from both sides.

$$x-x^{2}=-15x$$

Add 15x to both sides.

$$x-x^{2}+15x=0$$

Combine x and 15x to get 16x.

$$16x-x^{2}=0$$

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.

$$-x^{2}+16x=0$$

Divide both sides by -1.

$$\frac{-x^{2}+16x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{16}{-1}x=\frac{0}{-1}$$

Divide 16 by -1.

$$x^{2}-16x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}-16x=0$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=64$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{64}$$

Simplify.

$$x-8=8 x-8=-8$$

Add 8 to both sides of the equation.

$$x=16 x=0$$