Solve 14x^2+195x+658

$$14 { x }^{ 2 } +195x+658$$

Factor

$$14\left(x-\frac{-\sqrt{1177}-195}{28}\right)\left(x-\frac{\sqrt{1177}-195}{28}\right)$$

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.

$$14x^{2}+195x+658=0$$

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.

$$x=\frac{-195±\sqrt{195^{2}-4\times 14\times 658}}{2\times 14}$$

Square 195.

$$x=\frac{-195±\sqrt{38025-4\times 14\times 658}}{2\times 14}$$

Multiply -4 times 14.

$$x=\frac{-195±\sqrt{38025-56\times 658}}{2\times 14}$$

Multiply -56 times 658.

$$x=\frac{-195±\sqrt{38025-36848}}{2\times 14}$$

Add 38025 to -36848.

$$x=\frac{-195±\sqrt{1177}}{2\times 14}$$

Multiply 2 times 14.

$$x=\frac{-195±\sqrt{1177}}{28}$$

Now solve the equation x=\frac{-195±\sqrt{1177}}{28} when ± is plus. Add -195 to \sqrt{1177}.

$$x=\frac{\sqrt{1177}-195}{28}$$

Now solve the equation x=\frac{-195±\sqrt{1177}}{28} when ± is minus. Subtract \sqrt{1177} from -195.

$$x=\frac{-\sqrt{1177}-195}{28}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-195+\sqrt{1177}}{28} for x_{1} and \frac{-195-\sqrt{1177}}{28} for x_{2}.

$$14x^{2}+195x+658=14\left(x-\frac{\sqrt{1177}-195}{28}\right)\left(x-\frac{-\sqrt{1177}-195}{28}\right)$$

Evaluate

$$14x^{2}+195x+658$$