Solve m^2-11m-10^2

$$m ^ { 2 } - 11 m - 10 ^ { 2 }$$

Factor

$$\left(m-\frac{11-\sqrt{521}}{2}\right)\left(m-\frac{\sqrt{521}+11}{2}\right)$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$factor(m^{2}-11m-100)$$

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.

$$m^{2}-11m-100=0$$

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.

$$m=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-100\right)}}{2}$$

Square -11.

$$m=\frac{-\left(-11\right)±\sqrt{121-4\left(-100\right)}}{2}$$

Multiply -4 times -100.

$$m=\frac{-\left(-11\right)±\sqrt{121+400}}{2}$$

Add 121 to 400.

$$m=\frac{-\left(-11\right)±\sqrt{521}}{2}$$

The opposite of -11 is 11.

$$m=\frac{11±\sqrt{521}}{2}$$

Now solve the equation m=\frac{11±\sqrt{521}}{2} when ± is plus. Add 11 to \sqrt{521}.

$$m=\frac{\sqrt{521}+11}{2}$$

Now solve the equation m=\frac{11±\sqrt{521}}{2} when ± is minus. Subtract \sqrt{521} from 11.

$$m=\frac{11-\sqrt{521}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{11+\sqrt{521}}{2} for x_{1} and \frac{11-\sqrt{521}}{2} for x_{2}.

$$m^{2}-11m-100=\left(m-\frac{\sqrt{521}+11}{2}\right)\left(m-\frac{11-\sqrt{521}}{2}\right)$$

Evaluate

$$m^{2}-11m-100$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$m^{2}-11m-100$$