Solve 2x^2-45x-10=

$$2 { x }^{ 2 } -45x-10=$$

Factor

$$2\left(x-\frac{45-\sqrt{2105}}{4}\right)\left(x-\frac{\sqrt{2105}+45}{4}\right)$$

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.

$$2x^{2}-45x-10=0$$

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.

$$x=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\times 2\left(-10\right)}}{2\times 2}$$

Square -45.

$$x=\frac{-\left(-45\right)±\sqrt{2025-4\times 2\left(-10\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-45\right)±\sqrt{2025-8\left(-10\right)}}{2\times 2}$$

Multiply -8 times -10.

$$x=\frac{-\left(-45\right)±\sqrt{2025+80}}{2\times 2}$$

Add 2025 to 80.

$$x=\frac{-\left(-45\right)±\sqrt{2105}}{2\times 2}$$

The opposite of -45 is 45.

$$x=\frac{45±\sqrt{2105}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{45±\sqrt{2105}}{4}$$

Now solve the equation x=\frac{45±\sqrt{2105}}{4} when ± is plus. Add 45 to \sqrt{2105}.

$$x=\frac{\sqrt{2105}+45}{4}$$

Now solve the equation x=\frac{45±\sqrt{2105}}{4} when ± is minus. Subtract \sqrt{2105} from 45.

$$x=\frac{45-\sqrt{2105}}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{45+\sqrt{2105}}{4} for x_{1} and \frac{45-\sqrt{2105}}{4} for x_{2}.

$$2x^{2}-45x-10=2\left(x-\frac{\sqrt{2105}+45}{4}\right)\left(x-\frac{45-\sqrt{2105}}{4}\right)$$

Evaluate

$$2x^{2}-45x-10$$