Solve x^2-146x+900

$${ x }^{ 2 } -146x+900$$

Factor

$$\left(x-\left(73-\sqrt{4429}\right)\right)\left(x-\left(\sqrt{4429}+73\right)\right)$$

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.

$$x^{2}-146x+900=0$$

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.

$$x=\frac{-\left(-146\right)±\sqrt{\left(-146\right)^{2}-4\times 900}}{2}$$

Square -146.

$$x=\frac{-\left(-146\right)±\sqrt{21316-4\times 900}}{2}$$

Multiply -4 times 900.

$$x=\frac{-\left(-146\right)±\sqrt{21316-3600}}{2}$$

Add 21316 to -3600.

$$x=\frac{-\left(-146\right)±\sqrt{17716}}{2}$$

Take the square root of 17716.

$$x=\frac{-\left(-146\right)±2\sqrt{4429}}{2}$$

The opposite of -146 is 146.

$$x=\frac{146±2\sqrt{4429}}{2}$$

Now solve the equation x=\frac{146±2\sqrt{4429}}{2} when ± is plus. Add 146 to 2\sqrt{4429}.

$$x=\frac{2\sqrt{4429}+146}{2}$$

Divide 146+2\sqrt{4429} by 2.

$$x=\sqrt{4429}+73$$

Now solve the equation x=\frac{146±2\sqrt{4429}}{2} when ± is minus. Subtract 2\sqrt{4429} from 146.

$$x=\frac{146-2\sqrt{4429}}{2}$$

Divide 146-2\sqrt{4429} by 2.

$$x=73-\sqrt{4429}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 73+\sqrt{4429} for x_{1} and 73-\sqrt{4429} for x_{2}.

$$x^{2}-146x+900=\left(x-\left(\sqrt{4429}+73\right)\right)\left(x-\left(73-\sqrt{4429}\right)\right)$$

Evaluate

$$x^{2}-146x+900$$