Solve 2m^2-16m+108

$$2 { m }^{ 2 } -16m+108$$

Factor

$$2\left(m^{2}-8m+54\right)$$

Solution Steps

Factor out 2. Polynomial m^{2}-8m+54 is not factored since it does not have any rational roots.

$$2\left(m^{2}-8m+54\right)$$

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.

$$2m^{2}-16m+108=0$$

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.

$$m=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 2\times 108}}{2\times 2}$$

Square -16.

$$m=\frac{-\left(-16\right)±\sqrt{256-4\times 2\times 108}}{2\times 2}$$

Multiply -4 times 2.

$$m=\frac{-\left(-16\right)±\sqrt{256-8\times 108}}{2\times 2}$$

Multiply -8 times 108.

$$m=\frac{-\left(-16\right)±\sqrt{256-864}}{2\times 2}$$

Add 256 to -864.

$$m=\frac{-\left(-16\right)±\sqrt{-608}}{2\times 2}$$

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

$$2m^{2}-16m+108$$

Evaluate

$$2\left(m^{2}-8m+54\right)$$