Solve x^2+44x-7=

$${ x }^{ 2 } +44x-7=$$

Factor

$$\left(x-\left(-\sqrt{491}-22\right)\right)\left(x-\left(\sqrt{491}-22\right)\right)$$

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.

$$x^{2}+44x-7=0$$

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.

$$x=\frac{-44±\sqrt{44^{2}-4\left(-7\right)}}{2}$$

Square 44.

$$x=\frac{-44±\sqrt{1936-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$x=\frac{-44±\sqrt{1936+28}}{2}$$

Add 1936 to 28.

$$x=\frac{-44±\sqrt{1964}}{2}$$

Take the square root of 1964.

$$x=\frac{-44±2\sqrt{491}}{2}$$

Now solve the equation x=\frac{-44±2\sqrt{491}}{2} when ± is plus. Add -44 to 2\sqrt{491}.

$$x=\frac{2\sqrt{491}-44}{2}$$

Divide -44+2\sqrt{491} by 2.

$$x=\sqrt{491}-22$$

Now solve the equation x=\frac{-44±2\sqrt{491}}{2} when ± is minus. Subtract 2\sqrt{491} from -44.

$$x=\frac{-2\sqrt{491}-44}{2}$$

Divide -44-2\sqrt{491} by 2.

$$x=-\sqrt{491}-22$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -22+\sqrt{491} for x_{1} and -22-\sqrt{491} for x_{2}.

$$x^{2}+44x-7=\left(x-\left(\sqrt{491}-22\right)\right)\left(x-\left(-\sqrt{491}-22\right)\right)$$

Evaluate

$$x^{2}+44x-7$$