Solve 10x^2-100x+20000=

$$10 { x }^{ 2 } -100x+20000=$$

Factor

$$10\left(x^{2}-10x+2000\right)$$

Solution Steps

Factor out 10. Polynomial x^{2}-10x+2000 is not factored since it does not have any rational roots.

$$10\left(x^{2}-10x+2000\right)$$

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.

$$10x^{2}-100x+20000=0$$

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.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 10\times 20000}}{2\times 10}$$

Square -100.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4\times 10\times 20000}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-\left(-100\right)±\sqrt{10000-40\times 20000}}{2\times 10}$$

Multiply -40 times 20000.

$$x=\frac{-\left(-100\right)±\sqrt{10000-800000}}{2\times 10}$$

Add 10000 to -800000.

$$x=\frac{-\left(-100\right)±\sqrt{-790000}}{2\times 10}$$

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

$$10x^{2}-100x+20000$$

Evaluate

$$10\left(x^{2}-10x+2000\right)$$