Solve 256=96x-16x^2+256

$$256 = 96x-16 { x }^{ 2 } +256$$

Solve for x

$$x=6$$

$$x=0$$

Steps Using Factoring

Swap sides so that all variable terms are on the left hand side.

$$96x-16x^{2}+256=256$$

Subtract 256 from both sides.

$$96x-16x^{2}+256-256=0$$

Subtract 256 from 256 to get 0.

$$96x-16x^{2}=0$$

Factor out x.

$$x\left(96-16x\right)=0$$

To find equation solutions, solve x=0 and 96-16x=0.

$$x=0 x=6$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$96x-16x^{2}+256=256$$

Subtract 256 from both sides.

$$96x-16x^{2}+256-256=0$$

Subtract 256 from 256 to get 0.

$$96x-16x^{2}=0$$

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.

$$-16x^{2}+96x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 96 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-96±\sqrt{96^{2}}}{2\left(-16\right)}$$

Take the square root of 96^{2}.

$$x=\frac{-96±96}{2\left(-16\right)}$$

Multiply 2 times -16.

$$x=\frac{-96±96}{-32}$$

Now solve the equation x=\frac{-96±96}{-32} when ± is plus. Add -96 to 96.

$$x=\frac{0}{-32}$$

Divide 0 by -32.

$$x=0$$

Now solve the equation x=\frac{-96±96}{-32} when ± is minus. Subtract 96 from -96.

$$x=-\frac{192}{-32}$$

Divide -192 by -32.

$$x=6$$

The equation is now solved.

$$x=0 x=6$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

$$96x-16x^{2}+256=256$$

Subtract 256 from both sides.

$$96x-16x^{2}=256-256$$

Subtract 256 from 256 to get 0.

$$96x-16x^{2}=0$$

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.

$$-16x^{2}+96x=0$$

Divide both sides by -16.

$$\frac{-16x^{2}+96x}{-16}=\frac{0}{-16}$$

Dividing by -16 undoes the multiplication by -16.

$$x^{2}+\frac{96}{-16}x=\frac{0}{-16}$$

Divide 96 by -16.

$$x^{2}-6x=\frac{0}{-16}$$

Divide 0 by -16.

$$x^{2}-6x=0$$

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.

$$x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}$$

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.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Simplify.

$$x-3=3 x-3=-3$$

Add 3 to both sides of the equation.

$$x=6 x=0$$