Solve 5x+5x^2+5

$$5 x + 5 x ^ { 2 } + 5$$

Factor

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

Solution Steps

Factor out 5. Polynomial x+x^{2}+1 is not factored since it does not have any rational roots.

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

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.

$$5x^{2}+5x+5=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\times 5\times 5}}{2\times 5}$$

Square 5.

$$x=\frac{-5±\sqrt{25-4\times 5\times 5}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-5±\sqrt{25-20\times 5}}{2\times 5}$$

Multiply -20 times 5.

$$x=\frac{-5±\sqrt{25-100}}{2\times 5}$$

Add 25 to -100.

$$x=\frac{-5±\sqrt{-75}}{2\times 5}$$

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

$$5x^{2}+5x+5$$

Evaluate

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