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masha68 [24]
3 years ago
8

Which of the following is the result of the equation below after completing the square and factoring?

Mathematics
1 answer:
Tems11 [23]3 years ago
7 0

Answer:

D)  (x +  \frac{5}{2})^{2}   =  \frac{9}{4}

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation

             <em>   x² + 5 x + 8 = 4</em>

    ⇒        x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} -  (\frac{5}{2} )^{2}+ 8 = 4

<u><em>Step(ii):</em></u>-

    By using (a + b)² = a² + 2 a b + b²

  ⇒        (x +  \frac{5}{2})^{2}   -  (\frac{5}{2} )^{2}+ 8 = 4

  ⇒        (x +  \frac{5}{2})^{2}   = 4 + (\frac{5}{2} )^{2} -8

⇒           (x +  \frac{5}{2})^{2}   =  (\frac{25}{4} ) -4

⇒           (x +  \frac{5}{2})^{2}   =  (\frac{25-16}{4} )

⇒           (x +  \frac{5}{2})^{2}   =  \frac{9}{4}

<u><em>Final answer:-</em></u>

(x +  \frac{5}{2})^{2}   =  \frac{9}{4}

 

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