Solve 2x^2-196x-963

$$2 { x }^{ 2 } -196x-963$$

Factor

$$2\left(x-\left(-\frac{\sqrt{11530}}{2}+49\right)\right)\left(x-\left(\frac{\sqrt{11530}}{2}+49\right)\right)$$

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.

$$2x^{2}-196x-963=0$$

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.

$$x=\frac{-\left(-196\right)±\sqrt{\left(-196\right)^{2}-4\times 2\left(-963\right)}}{2\times 2}$$

Square -196.

$$x=\frac{-\left(-196\right)±\sqrt{38416-4\times 2\left(-963\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-196\right)±\sqrt{38416-8\left(-963\right)}}{2\times 2}$$

Multiply -8 times -963.

$$x=\frac{-\left(-196\right)±\sqrt{38416+7704}}{2\times 2}$$

Add 38416 to 7704.

$$x=\frac{-\left(-196\right)±\sqrt{46120}}{2\times 2}$$

Take the square root of 46120.

$$x=\frac{-\left(-196\right)±2\sqrt{11530}}{2\times 2}$$

The opposite of -196 is 196.

$$x=\frac{196±2\sqrt{11530}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{196±2\sqrt{11530}}{4}$$

Now solve the equation x=\frac{196±2\sqrt{11530}}{4} when ± is plus. Add 196 to 2\sqrt{11530}.

$$x=\frac{2\sqrt{11530}+196}{4}$$

Divide 196+2\sqrt{11530} by 4.

$$x=\frac{\sqrt{11530}}{2}+49$$

Now solve the equation x=\frac{196±2\sqrt{11530}}{4} when ± is minus. Subtract 2\sqrt{11530} from 196.

$$x=\frac{196-2\sqrt{11530}}{4}$$

Divide 196-2\sqrt{11530} by 4.

$$x=-\frac{\sqrt{11530}}{2}+49$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 49+\frac{\sqrt{11530}}{2} for x_{1} and 49-\frac{\sqrt{11530}}{2} for x_{2}.

$$2x^{2}-196x-963=2\left(x-\left(\frac{\sqrt{11530}}{2}+49\right)\right)\left(x-\left(-\frac{\sqrt{11530}}{2}+49\right)\right)$$

Evaluate

$$2x^{2}-196x-963$$