Question

What number would ypu add to both sides of x^2+7x=4 to complete the square

Answer 1

`(*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+7x=4\\\\x^2+2\cdot x\cdot3.5=4\ \ \ \ |+3.5^2\\\\\underbrace{x^2+2\cdot x\cdot3.5+3.5^2}_((*))=4+3.5^3\\\\(x+3.5)^2=16.25\\\\Answer:\ 3.5^2=12.25`

Answer 2

For a monic quadratic (factor of 1 on
`x^2`) we always add half the coefficient on the linear (
`x`) term, so

`\left(\frac 7 2\right)^2 = (49)/(4)`

Answer: 49/4

`x^2 + 7x + (49)/(4) = 4 + (49)/(4)`

`(x + \frac 7 2)^2 = 4 + (49)/(4)`