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disa [49]
2 years ago
5

X2 +1/2x+____=2+____?

Mathematics
1 answer:
quester [9]2 years ago
3 0

Answer:

x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2

Step-by-step explanation:

x^{2}+\frac{1}{2} x=x^{2}+2 \times \frac{1}{4} \times x  +(\frac{1}{4})^2 - (\frac{1}{4})^2

=[x^{2}+2 \times \frac{1}{4} \times x  +(\frac{1}{4})^2] - (\frac{1}{16})

=[x + \frac{1}{4}]^2 - (\frac{1}{16})

____________________

then

x^{2}+\frac{1}{2} x = [x + \frac{1}{4}]^2 - (\frac{1}{16}) -2 + 2

then

x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{1}{16}) -2] + 2

then

x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{33}{16}) ] + 2

then

x^{2}+\frac{1}{2} x = (x + \frac{1}{4})^2 - \frac{33}{16} + 2

then

x^{2}+\frac{1}{2} x + \frac{33}{16}= (x + \frac{1}{4})^2  + 2

then

x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2

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