Solve 5x^2-32x+2

$$5 { x }^{ 2 } -32x+2$$

Factor

$$5\left(x-\frac{16-\sqrt{246}}{5}\right)\left(x-\frac{\sqrt{246}+16}{5}\right)$$

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.

$$5x^{2}-32x+2=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 5\times 2}}{2\times 5}$$

Square -32.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\times 5\times 2}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-\left(-32\right)±\sqrt{1024-20\times 2}}{2\times 5}$$

Multiply -20 times 2.

$$x=\frac{-\left(-32\right)±\sqrt{1024-40}}{2\times 5}$$

Add 1024 to -40.

$$x=\frac{-\left(-32\right)±\sqrt{984}}{2\times 5}$$

Take the square root of 984.

$$x=\frac{-\left(-32\right)±2\sqrt{246}}{2\times 5}$$

The opposite of -32 is 32.

$$x=\frac{32±2\sqrt{246}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{32±2\sqrt{246}}{10}$$

Now solve the equation x=\frac{32±2\sqrt{246}}{10} when ± is plus. Add 32 to 2\sqrt{246}.

$$x=\frac{2\sqrt{246}+32}{10}$$

Divide 32+2\sqrt{246} by 10.

$$x=\frac{\sqrt{246}+16}{5}$$

Now solve the equation x=\frac{32±2\sqrt{246}}{10} when ± is minus. Subtract 2\sqrt{246} from 32.

$$x=\frac{32-2\sqrt{246}}{10}$$

Divide 32-2\sqrt{246} by 10.

$$x=\frac{16-\sqrt{246}}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{16+\sqrt{246}}{5} for x_{1} and \frac{16-\sqrt{246}}{5} for x_{2}.

$$5x^{2}-32x+2=5\left(x-\frac{\sqrt{246}+16}{5}\right)\left(x-\frac{16-\sqrt{246}}{5}\right)$$

Evaluate

$$5x^{2}-32x+2$$