Solve 6x^2+6x+3=

$$6 { x }^{ 2 } +6x+3=$$

Factor

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

Solution Steps

Factor out 3. Polynomial 2x^{2}+2x+1 is not factored since it does not have any rational roots.

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

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.

$$6x^{2}+6x+3=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 6\times 3}}{2\times 6}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 6\times 3}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-6±\sqrt{36-24\times 3}}{2\times 6}$$

Multiply -24 times 3.

$$x=\frac{-6±\sqrt{36-72}}{2\times 6}$$

Add 36 to -72.

$$x=\frac{-6±\sqrt{-36}}{2\times 6}$$

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

$$6x^{2}+6x+3$$

Evaluate

$$6x^{2}+6x+3$$