Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. 4x2 + 8x – 32 = 0

Answer 1

`4x^2 + 8x - 32 = 0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4`

Answer 2

For this case we must solve the following expression by completing squares:

`4x ^ 2 + 8x-32 = 0`

We divide between 4 on both sides of the equation:

`x ^ 2 + 2x-8 = 0`

We add 8 to both sides of the equation:

`x ^ 2 + 2x = 8`

We divide the middle term between 2 and square, this we add to both sides of the equation:

`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`

We apply root to both sides:

`x + 1 =\pm \sqrt {9}`

We have two roots:

`x_ {1} = \sqrt {9} -1 = 3-1 = 2\\x_ {2} = - \sqrt {9} -1 = -3-1 = -4`

Answer:

`x_ {1} = 2\\x_ {2} = - 4`