Question

x^ 2+5x+10=0. answer this question and get 10 points
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Answer 1

Answer:

$\red { Values \:of \: x } \green {= \frac{-5±\sqrt{5}}{2}}$

Step-by-step explanation:

$Given \: x^{2}+5x+10 = 0$

$\implies x^{2} + 5x = -10$

$\implies x^{2} + 2\times x \times \frac{5}{2} = -10$

$\implies x^{2} + 2\times x \times \frac{5}{2} + \left(\frac{5}{2}\right)^{2}= -10 + \left(\frac{5}{2}\right)^{2}$

$\implies \left( x + \frac{5}{2}\right)^{2} = -10 + \frac{25}{4}$

$\implies \left( x + \frac{5}{2}\right)^{2} =\\frac{-20+25}{4}$

$= \frac{5}{4}$

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

$\implies x = \frac{-5}{2} ±\frac{\sqrt{5}}{2}$

$= \frac{-5±\sqrt{5}}{2}$

Therefore.,

$\red { Values \:of \: x } \green {= \frac{-5±\sqrt{5}}{2}}$

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