Solve -x^2-5x+3

$$- { x }^{ 2 } -5x+3$$

Factor

$$-\left(x-\frac{-\sqrt{37}-5}{2}\right)\left(x-\frac{\sqrt{37}-5}{2}\right)$$

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.

$$-x^{2}-5x+3=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-5\right)±\sqrt{25+4\times 3}}{2\left(-1\right)}$$

Multiply 4 times 3.

$$x=\frac{-\left(-5\right)±\sqrt{25+12}}{2\left(-1\right)}$$

Add 25 to 12.

$$x=\frac{-\left(-5\right)±\sqrt{37}}{2\left(-1\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{37}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{5±\sqrt{37}}{-2}$$

Now solve the equation x=\frac{5±\sqrt{37}}{-2} when ± is plus. Add 5 to \sqrt{37}.

$$x=\frac{\sqrt{37}+5}{-2}$$

Divide 5+\sqrt{37} by -2.

$$x=\frac{-\sqrt{37}-5}{2}$$

Now solve the equation x=\frac{5±\sqrt{37}}{-2} when ± is minus. Subtract \sqrt{37} from 5.

$$x=\frac{5-\sqrt{37}}{-2}$$

Divide 5-\sqrt{37} by -2.

$$x=\frac{\sqrt{37}-5}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5-\sqrt{37}}{2} for x_{1} and \frac{-5+\sqrt{37}}{2} for x_{2}.

$$-x^{2}-5x+3=-\left(x-\frac{-\sqrt{37}-5}{2}\right)\left(x-\frac{\sqrt{37}-5}{2}\right)$$

Evaluate

$$3-5x-x^{2}$$