Solve 16x^2+32x+256

$$16 { x }^{ 2 } +32x+256$$

Factor

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

Solution Steps

Factor out 16. Polynomial x^{2}+2x+16 is not factored since it does not have any rational roots.

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

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$16x^{2}+32x+256=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4\times 16\times 256}}{2\times 16}$$

Square 32.

$$x=\frac{-32±\sqrt{1024-4\times 16\times 256}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{-32±\sqrt{1024-64\times 256}}{2\times 16}$$

Multiply -64 times 256.

$$x=\frac{-32±\sqrt{1024-16384}}{2\times 16}$$

Add 1024 to -16384.

$$x=\frac{-32±\sqrt{-15360}}{2\times 16}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

$$16x^{2}+32x+256$$

Evaluate

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