Question

Question #e9b10

Answer 1

`x = (-3+-sqrt10)/2`

Explanation:

To complete the square, the leading coefficient must be 1, therefore, we divide both sides by 4:

`x^2+ 3x - 1/4=0`

Move the constant term to the right side:

`x^2+ 3x = 1/4`

The pattern for a perfect square where the middle term is positive is, `(x+a)^2 = x^2 + 2ax+a^2`, therefore, we add `a^2` to both sides of the equation:

`x^2+ 3x +a^2=1/4+a^2`

Please observe that the left side of the equation matches the right side of the pattern.

We can find the value of "a" by setting the middle term of the pattern equal to the middle term of the equation:

`2ax = 3x`

`a = 3/2`

Because we know that the left side becomes a perfect square when `a=3/2`, we may substitute `(x + 3/2)^2` on the left and `3/2` for "a" on the right:

`(x + 3/2)^2=1/4+(3/2)^2`

Simplify the right side:

`(x + 3/2)^2=5/2`

Use the square root on both sides:

`x + 3/2=+-sqrt(5/2)`

Subtract `3/2` from both sides:

`x =-3/2+-sqrt(5/2)`

Simplify:

`x = (-3+-sqrt10)/2`

Answer 2

`x=(-6+-sqrt(37))/2`

Explanation:

`4x^2+12x+36-37=0`
`(2x+6)^2-37=0`
`(2x+6)^2=37`
`2x+6=+-sqrt(37)`
`2x=-6+-sqrt(37)`
`x=(-6+-sqrt(37))/2`