Question

Solving Quadratic Equations using the Square Root Property


`x^2+7x+10=0`

but the teacher's guide says the answer is 17i

Answer 1

`x = -2` or
`x = -5`

Explanation:

You need to complete the square before you can take the square root of both sides.

`x^2 + 7x + 10 = 0`

Subtract 10 from both sides.

`x^2 + 7x = -10`

To complete the square, you need to add the square of half of the x-term coefficient to both sides.

The x-term coefficient is 7. Half of that is 7/2. Square it to get 49/4. Now we add 49/4 to both sides of the equation.

`x^2 + 7x + (49)/(4) = -10 + (49)/(4)`

`(x + (7)/(2))^2 = -(40)/(4) + (49)/(4)`

`(x + (7)/(2))^2 = (9)/(4)`

Now we use the square root property, if

`x^2 = k`, then

`x = \pm √(k)`

`x + (7)/(2) = \pm \sqrt{(9)/(4)}`

`x + (7)/(2) = \pm (3)/(2)`

`x + (7)/(2) = (3)/(2)` or
`x + (7)/(2) = -(3)/(2)`

`x = -(4)/(2)` or
`x = -(10)/(2)`

`x = -2` or
`x = -5`