Solve 16x^2+18x+16

$$16 { x }^{ 2 } +18x+16$$

Factor

$$2\left(8x^{2}+9x+8\right)$$

Solution Steps

Factor out 2. Polynomial 8x^{2}+9x+8 is not factored since it does not have any rational roots.

$$2\left(8x^{2}+9x+8\right)$$

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.

$$16x^{2}+18x+16=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 16\times 16}}{2\times 16}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 16\times 16}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{-18±\sqrt{324-64\times 16}}{2\times 16}$$

Multiply -64 times 16.

$$x=\frac{-18±\sqrt{324-1024}}{2\times 16}$$

Add 324 to -1024.

$$x=\frac{-18±\sqrt{-700}}{2\times 16}$$

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

$$16x^{2}+18x+16$$

Evaluate

$$16x^{2}+18x+16$$