Respuesta :

What number will make y^2 + 2y + __ a perfect square? Take coefficient of y, divide by 2, then square it = (2/2)^2 = 1 So add 1 to both sides, since y^2 + 2y + 1 = (y + 1)^2 y^2 + 2y + 1 = 49
carlosego

For this case we have the following equation:

[tex]y ^ 2 + 2y = 48[/tex]

By completing squares we have:

Step 1:

Add [tex](\frac {b} {2}) ^ 2[/tex] on both sides:

[tex]y ^ 2 + 2y + 1 = 48 + 1[/tex]

Step 2:

We rewrite the equation:

[tex](y + 1) ^ 2 = 49[/tex]

Step 3:

We solve the equation:

[tex]y = \pm \sqrt {49} -1\\y = \pm7-1[/tex]

Solutions:

[tex]y = 6\\y = -8[/tex]

Answer:

the next line would be:

[tex]y ^ 2 + 2y + 1 = 48 + 1[/tex]


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