Solve 11x^2-121x

$$11 x ^ { 2 } - 121 x$$

Factor

$$11x\left(x-11\right)$$

Solution Steps

Factor out 11.

$$11\left(x^{2}-11x\right)$$

Consider x^{2}-11x. Factor out x.

$$x\left(x-11\right)$$

Rewrite the complete factored expression.

$$11x\left(x-11\right)$$

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.

$$11x^{2}-121x=0$$

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.

$$x=\frac{-\left(-121\right)±\sqrt{\left(-121\right)^{2}}}{2\times 11}$$

Take the square root of \left(-121\right)^{2}.

$$x=\frac{-\left(-121\right)±121}{2\times 11}$$

The opposite of -121 is 121.

$$x=\frac{121±121}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{121±121}{22}$$

Now solve the equation x=\frac{121±121}{22} when ± is plus. Add 121 to 121.

$$x=\frac{242}{22}$$

Divide 242 by 22.

$$x=11$$

Now solve the equation x=\frac{121±121}{22} when ± is minus. Subtract 121 from 121.

$$x=\frac{0}{22}$$

Divide 0 by 22.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 11 for x_{1} and 0 for x_{2}.

$$11x^{2}-121x=11\left(x-11\right)x$$

Evaluate

$$11x\left(x-11\right)$$