Solve 400x^2-400x+60000

$$400 { x }^{ 2 } -400x+60000$$

Factor

$$400\left(x^{2}-x+150\right)$$

Solution Steps

Factor out 400. Polynomial x^{2}-x+150 is not factored since it does not have any rational roots.

$$400\left(x^{2}-x+150\right)$$

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.

$$400x^{2}-400x+60000=0$$

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.

$$x=\frac{-\left(-400\right)±\sqrt{\left(-400\right)^{2}-4\times 400\times 60000}}{2\times 400}$$

Square -400.

$$x=\frac{-\left(-400\right)±\sqrt{160000-4\times 400\times 60000}}{2\times 400}$$

Multiply -4 times 400.

$$x=\frac{-\left(-400\right)±\sqrt{160000-1600\times 60000}}{2\times 400}$$

Multiply -1600 times 60000.

$$x=\frac{-\left(-400\right)±\sqrt{160000-96000000}}{2\times 400}$$

Add 160000 to -96000000.

$$x=\frac{-\left(-400\right)±\sqrt{-95840000}}{2\times 400}$$

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

$$400x^{2}-400x+60000$$

Evaluate

$$400\left(x^{2}-x+150\right)$$