Question

Complete the square: x2+7x+?=(x+?)2

Answer 1

Answer:

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

Explanation:

${x}^{2} + 7x + a = {(x + b)}^{2}$

${x}^{2} + 7x + a = {x}^{2} + 2bx + {b}^{2}$

compare the x co-efficient

$7 = 2b$

$b = \frac{7}{2}$

compare the constants

$a = {b}^{2}$

$a = {( \frac{7}{2}) }^{2}$

$a = \frac{49}{4}$