Solve {l}{x^2-60x}{+1,00}

$$\left. \begin{array} { l } { x ^ { 2 } - 60 x } \\ { + 1,00 } \end{array} \right.$$

Factor

$$\left(x-\left(30-\sqrt{899}\right)\right)\left(x-\left(\sqrt{899}+30\right)\right)$$

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.

$$x^{2}-60x+1=0$$

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.

$$x=\frac{-\left(-60\right)±\sqrt{\left(-60\right)^{2}-4}}{2}$$

Square -60.

$$x=\frac{-\left(-60\right)±\sqrt{3600-4}}{2}$$

Add 3600 to -4.

$$x=\frac{-\left(-60\right)±\sqrt{3596}}{2}$$

Take the square root of 3596.

$$x=\frac{-\left(-60\right)±2\sqrt{899}}{2}$$

The opposite of -60 is 60.

$$x=\frac{60±2\sqrt{899}}{2}$$

Now solve the equation x=\frac{60±2\sqrt{899}}{2} when ± is plus. Add 60 to 2\sqrt{899}.

$$x=\frac{2\sqrt{899}+60}{2}$$

Divide 60+2\sqrt{899} by 2.

$$x=\sqrt{899}+30$$

Now solve the equation x=\frac{60±2\sqrt{899}}{2} when ± is minus. Subtract 2\sqrt{899} from 60.

$$x=\frac{60-2\sqrt{899}}{2}$$

Divide 60-2\sqrt{899} by 2.

$$x=30-\sqrt{899}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 30+\sqrt{899} for x_{1} and 30-\sqrt{899} for x_{2}.

$$x^{2}-60x+1=\left(x-\left(\sqrt{899}+30\right)\right)\left(x-\left(30-\sqrt{899}\right)\right)$$

Evaluate

$$x^{2}-60x+1$$