Solve x^2+14x+3

$${ x }^{ 2 } +14x+3$$

Factor

$$\left(x-\left(-\sqrt{46}-7\right)\right)\left(x-\left(\sqrt{46}-7\right)\right)$$

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.

$$x^{2}+14x+3=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 3}}{2}$$

Square 14.

$$x=\frac{-14±\sqrt{196-4\times 3}}{2}$$

Multiply -4 times 3.

$$x=\frac{-14±\sqrt{196-12}}{2}$$

Add 196 to -12.

$$x=\frac{-14±\sqrt{184}}{2}$$

Take the square root of 184.

$$x=\frac{-14±2\sqrt{46}}{2}$$

Now solve the equation x=\frac{-14±2\sqrt{46}}{2} when ± is plus. Add -14 to 2\sqrt{46}.

$$x=\frac{2\sqrt{46}-14}{2}$$

Divide -14+2\sqrt{46} by 2.

$$x=\sqrt{46}-7$$

Now solve the equation x=\frac{-14±2\sqrt{46}}{2} when ± is minus. Subtract 2\sqrt{46} from -14.

$$x=\frac{-2\sqrt{46}-14}{2}$$

Divide -14-2\sqrt{46} by 2.

$$x=-\sqrt{46}-7$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -7+\sqrt{46} for x_{1} and -7-\sqrt{46} for x_{2}.

$$x^{2}+14x+3=\left(x-\left(\sqrt{46}-7\right)\right)\left(x-\left(-\sqrt{46}-7\right)\right)$$

Evaluate

$$x^{2}+14x+3$$