# Solve quadratic equation using the quadratic formula. x^2 + 5x + 2 = 0

Question
Solve quadratic equation using the quadratic formula. $$\displaystyle{x}^{{2}}+{5}{x}+{2}={0}$$

2020-12-04
The quadratic formula used for quadratic equation $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$ is,
$$\displaystyle{x}=-\frac{{{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}$$
Here, a=1, b=5 ,c=2
Substitute the given values in the quadratic formula as,
$$\displaystyle{x}=\frac{{-{5}\pm\sqrt{{{25}-{20}}}}}{{2}}$$
$$\displaystyle{x}=\frac{{-{5}\pm\sqrt{{5}}}}{{2}}$$
Hence, the solution for the equation is $$\displaystyle{x}=\frac{{-{5}+\sqrt{{5}}}}{{2}}{\quad\text{and}\quad}{x}=\frac{{-{5}-\sqrt{{5}}}}{{2}}$$

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