Question on: SS2 Mathematics - Simultaneous Linear and Quadratic Equations
Solve the equation \(x^{2} + 5x + 4 = 0\) using the completing the square method
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A
x = 2 or 1
B
x = 1 or -4
C
x = -4 or -1
D
x = 2 or -2
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Correct Option: C
\[x^{2} + 5x + 4 = 0\]
\[x^{2} + 5x = - 4\]
\[x^{2} + 5x + \left( \frac{5}{2} \right)^{2} = \left( \frac{5}{2} \right)^{2} - 4\]
\[x^{2} + 5x + \frac{25}{4} = \frac{25}{4} - 4\]
\[{(x + \frac{5}{2})}^{2} = \frac{9}{4}\]
\[x + \frac{5}{2} = \pm \sqrt{\frac{9}{4}} = \pm \frac{3}{2}\]
\[x + \frac{5}{2} = \pm \frac{3}{2}\]
\[x = \frac{3}{2} - \frac{5}{2}\ or - \frac{3}{2} - \frac{5}{2}\]
\[x = \frac{3 - 5}{2}\ or\frac{- 3 - 5}{2}\]
\[x = \frac{- 2}{2}\ or\frac{- 8}{2}\]
\(x = - 1\ or - 4\)
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