Solve 25x^2-10x+5

$$25 { x }^{ 2 } -10x+5$$

Factor

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

Solution Steps

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

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

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.

$$25x^{2}-10x+5=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 25\times 5}}{2\times 25}$$

Square -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 25\times 5}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{-\left(-10\right)±\sqrt{100-100\times 5}}{2\times 25}$$

Multiply -100 times 5.

$$x=\frac{-\left(-10\right)±\sqrt{100-500}}{2\times 25}$$

Add 100 to -500.

$$x=\frac{-\left(-10\right)±\sqrt{-400}}{2\times 25}$$

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

$$25x^{2}-10x+5$$

Evaluate

$$25x^{2}-10x+5$$