Solve 10x^2-480x+5856

$$10 { x }^{ 2 } -480x+5856$$

Factor

$$2\left(5x^{2}-240x+2928\right)$$

Solution Steps

Factor out 2. Polynomial 5x^{2}-240x+2928 is not factored since it does not have any rational roots.

$$2\left(5x^{2}-240x+2928\right)$$

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.

$$10x^{2}-480x+5856=0$$

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.

$$x=\frac{-\left(-480\right)±\sqrt{\left(-480\right)^{2}-4\times 10\times 5856}}{2\times 10}$$

Square -480.

$$x=\frac{-\left(-480\right)±\sqrt{230400-4\times 10\times 5856}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-\left(-480\right)±\sqrt{230400-40\times 5856}}{2\times 10}$$

Multiply -40 times 5856.

$$x=\frac{-\left(-480\right)±\sqrt{230400-234240}}{2\times 10}$$

Add 230400 to -234240.

$$x=\frac{-\left(-480\right)±\sqrt{-3840}}{2\times 10}$$

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

$$10x^{2}-480x+5856$$

Evaluate

$$10x^{2}-480x+5856$$