Solve 11*5x^2+82x-4

$$11 \cdot 5 x ^ { 2 } + 82 x - 4$$

Factor

$$55\left(x-\frac{-\sqrt{1901}-41}{55}\right)\left(x-\frac{\sqrt{1901}-41}{55}\right)$$

Steps Using the Quadratic Formula

Multiply 11 and 5 to get 55.

$$factor(55x^{2}+82x-4)$$

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.

$$55x^{2}+82x-4=0$$

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.

$$x=\frac{-82±\sqrt{82^{2}-4\times 55\left(-4\right)}}{2\times 55}$$

Square 82.

$$x=\frac{-82±\sqrt{6724-4\times 55\left(-4\right)}}{2\times 55}$$

Multiply -4 times 55.

$$x=\frac{-82±\sqrt{6724-220\left(-4\right)}}{2\times 55}$$

Multiply -220 times -4.

$$x=\frac{-82±\sqrt{6724+880}}{2\times 55}$$

Add 6724 to 880.

$$x=\frac{-82±\sqrt{7604}}{2\times 55}$$

Take the square root of 7604.

$$x=\frac{-82±2\sqrt{1901}}{2\times 55}$$

Multiply 2 times 55.

$$x=\frac{-82±2\sqrt{1901}}{110}$$

Now solve the equation x=\frac{-82±2\sqrt{1901}}{110} when ± is plus. Add -82 to 2\sqrt{1901}.

$$x=\frac{2\sqrt{1901}-82}{110}$$

Divide -82+2\sqrt{1901} by 110.

$$x=\frac{\sqrt{1901}-41}{55}$$

Now solve the equation x=\frac{-82±2\sqrt{1901}}{110} when ± is minus. Subtract 2\sqrt{1901} from -82.

$$x=\frac{-2\sqrt{1901}-82}{110}$$

Divide -82-2\sqrt{1901} by 110.

$$x=\frac{-\sqrt{1901}-41}{55}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-41+\sqrt{1901}}{55} for x_{1} and \frac{-41-\sqrt{1901}}{55} for x_{2}.

$$55x^{2}+82x-4=55\left(x-\frac{\sqrt{1901}-41}{55}\right)\left(x-\frac{-\sqrt{1901}-41}{55}\right)$$

Evaluate

$$55x^{2}+82x-4$$

Solution Steps

Multiply 11 and 5 to get 55.

$$55x^{2}+82x-4$$