identify terms for the quadratic formula, then solve for x. $x^{2}+4x + 5 = 0$ for $ax^{2}+bx + c = 0$…

identify terms for the quadratic formula, then solve for x. $x^{2}+4x + 5 = 0$ for $ax^{2}+bx + c = 0$ $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$ $a = 1$ $b = 4$ $c = 5$ $-b=-4$ $4ac = 20$ $b^{2}=16$ $2a = 2$ $x=\frac{pmsqrt{}}{}$

identify terms for the quadratic formula, then solve for x. $x^{2}+4x + 5 = 0$ for $ax^{2}+bx + c = 0$ $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$ $a = 1$ $b = 4$ $c = 5$ $-b=-4$ $4ac = 20$ $b^{2}=16$ $2a = 2$ $x=\frac{pmsqrt{}}{}$

Answer

Explanation:

Step1: Substitute values into quadratic formula

Given (a = 1), (b = 4), (c = 5), substitute into (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}). So (x=\frac{-4\pm\sqrt{16 - 20}}{2}).

Step2: Simplify the expression under the square - root

Calculate (b^{2}-4ac=16 - 20=-4). So (x=\frac{-4\pm\sqrt{-4}}{2}). Since (\sqrt{-4}=\sqrt{4\times(- 1)} = 2i) (where (i=\sqrt{-1})), then (x=\frac{-4\pm2i}{2}).

Step3: Simplify the fraction

Divide each term in the numerator by 2. (x=\frac{-4}{2}\pm\frac{2i}{2}=-2\pm i).

Answer:

(x=-2\pm i)