Respuesta :
Answer:
The number 49/4 should be added on both sides of [tex]x^2 + 7x = 4[/tex] to complete the square.
Step-by-step explanation:
[tex]x^{2} + 7x +\frac{49}{4} = 4 + \frac{49}{4}[/tex]
[tex]{4x^{2} + 28x + \frac{49}{4} = {16 + \frac{49}{4}[/tex]
[tex]{4x^{2} + 28x + 49} = 16 + 49[/tex]
[tex](2x + 7)2 = 65[/tex] [since [tex]a^{2} + 2ab + b^{2} = (a + b)^{2}[/tex]]
[tex](2x + 7)^{2}[/tex] [tex]=[/tex] [tex](\sqrt65)^2[/tex]
Answer:
See below
Step-by-step explanation:
x^2 + 7x - 4 = 0 take 1/2 of the 'x ' coefficient (this is 7/2) and do this:
(x + 7/2)^2 -4 now when you expand this (see botom line) you will see you have added 49/4 to the equation....you will need to subtract this for the equation to be the same :
(x+7/2)^2 - 49/4 - 4 = 0 then simplify to:
(x+7/2)^2 - 65/4 = 0 you can re-arrange if needed to this:
(x+7/2)^2 = 65/4
(x+7/2)^2 = x^2 + 7x + 49/4 <====== this needs to be subtracted
