Solve x^2+5x-4+2

$$x ^ { 2 } + 5 x - 4 + 2$$

Factor

$$\left(x-\frac{-\sqrt{33}-5}{2}\right)\left(x-\frac{\sqrt{33}-5}{2}\right)$$

Steps Using the Quadratic Formula

Add -4 and 2 to get -2.

$$factor(x^{2}+5x-2)$$

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.

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

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.

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

Square 5.

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

Multiply -4 times -2.

$$x=\frac{-5±\sqrt{25+8}}{2}$$

Add 25 to 8.

$$x=\frac{-5±\sqrt{33}}{2}$$

Now solve the equation x=\frac{-5±\sqrt{33}}{2} when ± is plus. Add -5 to \sqrt{33}.

$$x=\frac{\sqrt{33}-5}{2}$$

Now solve the equation x=\frac{-5±\sqrt{33}}{2} when ± is minus. Subtract \sqrt{33} from -5.

$$x=\frac{-\sqrt{33}-5}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+\sqrt{33}}{2} for x_{1} and \frac{-5-\sqrt{33}}{2} for x_{2}.

$$x^{2}+5x-2=\left(x-\frac{\sqrt{33}-5}{2}\right)\left(x-\frac{-\sqrt{33}-5}{2}\right)$$

Evaluate

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

Solution Steps

Add -4 and 2 to get -2.

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