Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Step(i):-

Given equation

                x² + 5 x + 8 = 4

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

Step(ii):-

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

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

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

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

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

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

Final answer:-

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