Solve 3x^2+15x+3

$$3 { x }^{ 2 } +15x+3$$

Factor

$$3\left(x-\frac{-\sqrt{21}-5}{2}\right)\left(x-\frac{\sqrt{21}-5}{2}\right)$$

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.

$$3x^{2}+15x+3=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 3\times 3}}{2\times 3}$$

Square 15.

$$x=\frac{-15±\sqrt{225-4\times 3\times 3}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-15±\sqrt{225-12\times 3}}{2\times 3}$$

Multiply -12 times 3.

$$x=\frac{-15±\sqrt{225-36}}{2\times 3}$$

Add 225 to -36.

$$x=\frac{-15±\sqrt{189}}{2\times 3}$$

Take the square root of 189.

$$x=\frac{-15±3\sqrt{21}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-15±3\sqrt{21}}{6}$$

Now solve the equation x=\frac{-15±3\sqrt{21}}{6} when ± is plus. Add -15 to 3\sqrt{21}.

$$x=\frac{3\sqrt{21}-15}{6}$$

Divide -15+3\sqrt{21} by 6.

$$x=\frac{\sqrt{21}-5}{2}$$

Now solve the equation x=\frac{-15±3\sqrt{21}}{6} when ± is minus. Subtract 3\sqrt{21} from -15.

$$x=\frac{-3\sqrt{21}-15}{6}$$

Divide -15-3\sqrt{21} by 6.

$$x=\frac{-\sqrt{21}-5}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+\sqrt{21}}{2} for x_{1} and \frac{-5-\sqrt{21}}{2} for x_{2}.

$$3x^{2}+15x+3=3\left(x-\frac{\sqrt{21}-5}{2}\right)\left(x-\frac{-\sqrt{21}-5}{2}\right)$$

Evaluate

$$3\left(x^{2}+5x+1\right)$$