For this case we must solve the following expression by completing squares:
[tex]4x ^ 2 + 8x-32 = 0[/tex]
We divide between 4 on both sides of the equation:
[tex]x ^ 2 + 2x-8 = 0[/tex]
We add 8 to both sides of the equation:
[tex]x ^ 2 + 2x = 8[/tex]
We divide the middle term between 2 and square, this we add to both sides of the equation:
[tex]x ^ 2 + 2x + (\frac {2} {2}) ^ 2 = 8 + (\frac {2} {2}) ^ 2\\x ^ 2 + 2x + 1 ^ 2 = 8 + 1\\x ^ 2 + 2x + 1 ^ 2 = 9\\(x + 1) ^ 2 = 9[/tex]
We apply root to both sides:
[tex]x + 1 =\pm \sqrt {9}[/tex]
We have two roots:
[tex]x_ {1} = \sqrt {9} -1 = 3-1 = 2\\x_ {2} = - \sqrt {9} -1 = -3-1 = -4[/tex]
Answer:
[tex]x_ {1} = 2\\x_ {2} = - 4[/tex]
