Solve 16x^2+64x+80

$$16 { x }^{ 2 } +64x+80$$

Factor

$$16\left(x^{2}+4x+5\right)$$

Solution Steps

Factor out 16. Polynomial x^{2}+4x+5 is not factored since it does not have any rational roots.

$$16\left(x^{2}+4x+5\right)$$

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.

$$16x^{2}+64x+80=0$$

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.

$$x=\frac{-64±\sqrt{64^{2}-4\times 16\times 80}}{2\times 16}$$

Square 64.

$$x=\frac{-64±\sqrt{4096-4\times 16\times 80}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{-64±\sqrt{4096-64\times 80}}{2\times 16}$$

Multiply -64 times 80.

$$x=\frac{-64±\sqrt{4096-5120}}{2\times 16}$$

Add 4096 to -5120.

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

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

$$16x^{2}+64x+80$$

Evaluate

$$16\left(x^{2}+4x+5\right)$$