Solve 5x^2+15x+25

$$5 { x }^{ 2 } +15x+25$$

Factor

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

Solution Steps

Factor out 5. Polynomial x^{2}+3x+5 is not factored since it does not have any rational roots.

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

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.

$$5x^{2}+15x+25=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 5\times 25}}{2\times 5}$$

Square 15.

$$x=\frac{-15±\sqrt{225-4\times 5\times 25}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-15±\sqrt{225-20\times 25}}{2\times 5}$$

Multiply -20 times 25.

$$x=\frac{-15±\sqrt{225-500}}{2\times 5}$$

Add 225 to -500.

$$x=\frac{-15±\sqrt{-275}}{2\times 5}$$

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

$$5x^{2}+15x+25$$

Evaluate

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