Solve 5a^2+5a+11a+6

$$5 a ^ { 2 } + 5 a + 11 a + 6$$

Factor

$$5\left(a-\frac{-\sqrt{34}-8}{5}\right)\left(a-\frac{\sqrt{34}-8}{5}\right)$$

Steps Using the Quadratic Formula

Combine 5a and 11a to get 16a.

$$factor(5a^{2}+16a+6)$$

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.

$$5a^{2}+16a+6=0$$

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.

$$a=\frac{-16±\sqrt{16^{2}-4\times 5\times 6}}{2\times 5}$$

Square 16.

$$a=\frac{-16±\sqrt{256-4\times 5\times 6}}{2\times 5}$$

Multiply -4 times 5.

$$a=\frac{-16±\sqrt{256-20\times 6}}{2\times 5}$$

Multiply -20 times 6.

$$a=\frac{-16±\sqrt{256-120}}{2\times 5}$$

Add 256 to -120.

$$a=\frac{-16±\sqrt{136}}{2\times 5}$$

Take the square root of 136.

$$a=\frac{-16±2\sqrt{34}}{2\times 5}$$

Multiply 2 times 5.

$$a=\frac{-16±2\sqrt{34}}{10}$$

Now solve the equation a=\frac{-16±2\sqrt{34}}{10} when ± is plus. Add -16 to 2\sqrt{34}.

$$a=\frac{2\sqrt{34}-16}{10}$$

Divide -16+2\sqrt{34} by 10.

$$a=\frac{\sqrt{34}-8}{5}$$

Now solve the equation a=\frac{-16±2\sqrt{34}}{10} when ± is minus. Subtract 2\sqrt{34} from -16.

$$a=\frac{-2\sqrt{34}-16}{10}$$

Divide -16-2\sqrt{34} by 10.

$$a=\frac{-\sqrt{34}-8}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-8+\sqrt{34}}{5} for x_{1} and \frac{-8-\sqrt{34}}{5} for x_{2}.

$$5a^{2}+16a+6=5\left(a-\frac{\sqrt{34}-8}{5}\right)\left(a-\frac{-\sqrt{34}-8}{5}\right)$$

Evaluate

$$5a^{2}+16a+6$$

Solution Steps

Combine 5a and 11a to get 16a.

$$5a^{2}+16a+6$$