$y = x^{2} + 7 x - 5$ can be written in the form $y = (x + a)^{2} +$ b Find the value of $a$ and the value of $b$

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Solution

$x^{2} + 7 x - 5$

$= x^{2} + 2. (\frac{7}{2}) x + {(\frac{7}{2})}^{2} {(\frac{7}{2})}^{2} - 5$

$= {(x + \frac{7}{2})}^{2} - (\frac{49}{4} + 5)$

$= {(x + \frac{7}{2})}^{2} - (\frac{49 + 20}{4})$

$= {(x + \frac{7}{2})}^{2} - (\frac{69}{4})$

$= (x + a)^{2} + b$

$∴ a = 7 / 2$ and $b = - 69 / 4.$

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y=x2+7x−5 can be written in the form y=(x+a)2+ b Find the value of a and the value of b

x2+7x−5=x2+2.(72)x+(72)2(72)2−5=(x+72)2−(494+5)=(x+72)2−(49+204)=(x+72)2−(694)=(x+a)2+b∴a=7/2 and b=−69/4.

$y = x^{2} + 7 x - 5$ can be written in the form $y = (x + a)^{2} +$ b Find the value of $a$ and the value of $b$