Question

find the roots of the following quadratic equation if they exist by the method of completing the square
x2+x-4

Answer 1

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Answer 2

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ {x}^{2} + x - 4 = 0 \\ {x}^{2} + 2 \times \frac{1}{2} \times x = 4 \\ adding \: {( \frac{1}{2}) }^{2} \: on \: both \: sides \\ {x}^{2} + 2 \times \frac{1}{2} \times x + \frac{1}{4} = 4 + \frac{1}{4 } \\ {x}^{2} + 2 \times \frac{1}{2} \times x = \frac{17}{4} \\ {(x + \frac{1}{2}) }^{2} = ( {\frac{ | \sqrt{17} | }{2} } )^ {2} \\ x + \frac{1}{2} = \frac{ | \sqrt{17} | }{2} \\ x = \frac{ | \sqrt{17} | - 1}{2}$
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