Solve 50-37x+x^2

$$50-37x+ { x }^{ 2 }$$

Factor

$$\left(x-\frac{37-\sqrt{1169}}{2}\right)\left(x-\frac{\sqrt{1169}+37}{2}\right)$$

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.

$$x^{2}-37x+50=0$$

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.

$$x=\frac{-\left(-37\right)±\sqrt{\left(-37\right)^{2}-4\times 50}}{2}$$

Square -37.

$$x=\frac{-\left(-37\right)±\sqrt{1369-4\times 50}}{2}$$

Multiply -4 times 50.

$$x=\frac{-\left(-37\right)±\sqrt{1369-200}}{2}$$

Add 1369 to -200.

$$x=\frac{-\left(-37\right)±\sqrt{1169}}{2}$$

The opposite of -37 is 37.

$$x=\frac{37±\sqrt{1169}}{2}$$

Now solve the equation x=\frac{37±\sqrt{1169}}{2} when ± is plus. Add 37 to \sqrt{1169}.

$$x=\frac{\sqrt{1169}+37}{2}$$

Now solve the equation x=\frac{37±\sqrt{1169}}{2} when ± is minus. Subtract \sqrt{1169} from 37.

$$x=\frac{37-\sqrt{1169}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{37+\sqrt{1169}}{2} for x_{1} and \frac{37-\sqrt{1169}}{2} for x_{2}.

$$x^{2}-37x+50=\left(x-\frac{\sqrt{1169}+37}{2}\right)\left(x-\frac{37-\sqrt{1169}}{2}\right)$$

Evaluate

$$x^{2}-37x+50$$